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Probabilistic Mechanics of Quasibrittle Structures
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Book description

Quasibrittle (or brittle heterogeneous) materials are becoming increasingly important for modern engineering. They include concretes, rocks, fiber composites, tough ceramics, sea ice, bone, wood, stiff soils, rigid foams, glass, dental and biomaterials, as well as all brittle materials on the micro or nano scale. Their salient feature is that the fracture process zone size is non-negligible compared to the structural dimensions. This causes intricate energetic and statistical size effects and leads to size-dependent probability distribution of strength, transitional between Gaussian and Weibullian. The ensuing difficult challenges for safe design are vanquished in this book, which features a rigorous theory with detailed derivations yet no superfluous mathematical sophistication; extensive experimental verifications; and realistic approximations for design. A wide range of subjects is covered, including probabilistic fracture kinetics at nanoscale, multiscale transition, statistics of structural strength and lifetime, size effect, reliability indices, safety factors, and ramification to gate dielectrics breakdown.

Reviews

'This new book provides a welcome addition to the very sparse collection of contemporary books that genuinely move the field of mechanics and materials forward. It does so by major steps of progress and consolidation, not just by incremental change. And its beneficial effects are not limited to mechanics and materials. … Virtually all work is supported by experimental verification. There is an unusually large, detailed and illuminating summary of past work and references. Much of it is from the senior author’s voluminous and well received contributions to the research literature. As is evident, this is a research oriented book. It is not for beginners. But for those interested in the topic and determined to diligently pursue it, then this book will prove to be an invaluable and indispensable resource. The authors seem to have been committed to work on some of the very hardest problems in existence and their progress is nothing short of remarkable.'

Richard M. Christensen Source: Meccanica

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References
Abadeer, W.W., Bagramian, A., Conkie, D. M., Griffin, C.W., Langlois, E., Lloyd, B. F., Mallette, R. P., Massucco, J. E., Mckenna, J. M., Mittl, S. W., & Noel, P. H. (1999). Key measurements of ultrathin gate dielectric reliability and in-line monitoring. IBM J. Res. Dev. 43(3), 407– 416.
Abraham, F. F., Broughton, J. Q., Bernstein, N., & Kaxiras, E. (1998). Spanning the continuum to quantum length scales in a dynamical simulation of brittle fracture. Europhys. Lett. 44(6), 783– 787.
Aifantis, E. C. (1984). On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. ASME 106, 326–330.
Akisanya, A. R., & Fleck, N. A. (1997). Interfacial cracking from the free-edge of a long bimaterial strip. Int. J. Solids Struct. 34(13), 1645–1665.
American Association of State Highway and Transportation Officials (2010). Standard method of test for performance graded asphalt binder, AASHTO M320-10-UL, Washington, D.C.
American Concrete Institute Committee 318 (2011). ACI318-11 Building Code Requirement for Structural Concrete and Commentary, Farmington Hills, MI.
American Institute of Steel Construction (2011). Steel Construction Manual.
Andersons, J., Hojo, M., & Ochiai, S. (2004). Empirical model for stress ratio effect on fatigue delamination growth rate in composite laminates. Int. J. Fatigue 26, 597–604.
Ang, A. H. S., & Tang, W. H. (1984). Probability Concepts in Engineering Planning and Design. Vol II: Decision, Risk and Reliability. John Wiley & Sons, New York.
Apte, P. P., & Saraswat, K. C. (1994). Correlation of trap generation to charge-to-breakdown (qbd): A physical-damage model of dielectric breakdown. IEEE Trans. Electron Dev. 41, 1595– 1602.
Atkinson, B. K. (1984). Subcritical crack growth in geological materials. J. Geophys. Res. 89(B6), 4077–4114.
Award, M. E., & Hilsdorf, H. K. (1972). Strength and deformation characteristics of plain concrete subjected to high repeated and sustained loads. In Proceedings of Abeles Symposium: Fatigue of Concrete, Hollywood, FL and Atlantic City, NJ, pp. 1–13.
Ayyub, B. M., & Haldar, A. (1984). Practical structural reliability techniques. J. Struct. Eng.- ASCE 110(8), 1707–1724.
Aziz, M. J., Sabin, P. C., & Lu, G. Q. (1991). The activation strain tensor: Nonhydrostatic stress effects on crystal growth kinetics. Phys. Rev. B 41, 9812–9816.
Bao, G., & Suo, Z. (1992). Remarks on crack-bridging concepts. Appl. Mech. Rev. 45, 355–366.
Barenblatt, G. I. (1959). The formation of equilibrium cracks during brittle fracture, general ideas and hypothesis, axially symmetric cracks. Prikl. Mat. Mech. 23(3), 434–444.
Barenblatt, G. I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129.
Barenblatt, G. I. (1979). Similarity, Self-Similarity and Intermediate Asymptotics. Consultants Bureau, New York.
Barenblatt, G. I. (1987). Dimensional Analysis. Gordon and Breach, New York.
Barenblatt, G. I. (1996). Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge.
Barenblatt, G. I. (2003). Scaling. Cambridge University Press, Cambridge.
Barenblatt, G. I. (2014). Flow, Deformation and Fracture. Cambridge University Press, Cambridge, U.K.
Barenblatt, G. I., & Botvina, L. R. (1981). Incomplete self-similarity of fatigue in the linear range of crack growth. Fatigue Fract. Eng. Mater. Struct. 3, 193–212.
Barsoum, R. S. (2003). The best of both worlds: Hybrid ship hulls use composites & steel. AMPTIAC Q. 7(3), 55–61.
Bartle, A. (1985). Four major dam failures re-examined. Int. Water Power Dam Constr. 37(11), 33–36, 41–46.
Basquin, O. H. (1910). The exponential law of endurance tests. Proc. Am. Soc. Test. Mater. ASTE 10, 625–630.
Batdorf, S. B. (1982). Tensile strength of unidirectionally reinforced composites. J. Reinf. Plast. Compos. 1, 153–164.
Bažant, Z. P. (1976). Instability, ductility, and size effect in strain-softening concrete. J. Eng. Mech. Div. ASCE 102, EM2, 331–344.
Bažant, Z. P. (1982). Crack band model for fracture of geomaterials. In Z., Eisenstein (ed.), Proceedings of the 4th International Conference on Numerical Methods in Geomechanics, Vol. 3. Edmonton, Alberta, pp. 1137–1152.
Bažant, Z. P. (1984a). Imbricate continuum and progressive fracturing of concrete and geomaterials. Meccanica 19, 86–93.
Bažant, Z. P. (1984b). Size effect in blunt fracture: Concrete, rock, metal. J. Eng. Mech. ASCE 110(4), 518–535.
Bažant, Z. P. (1992a). Large-scale thermal bending fracture of sea ice plates. J. Geophys. Res. (Oceans) 97(C11), 17739–17751.
Bažant, Z. P., ed. (1992b). Fracture Mechanics of Concrete Structures: Proceedings of the First International Conference, Elsevier, London.
Bažant, Z. P. (1993). Scaling laws in mechanics of fracture. J. Eng. Mech. ASCE 119(9), 1828– 1844.
Bažant, Z. P. (1996). Size effect aspects of measurement of fracture characteristics of quasibrittle material. Adv. Cem. Based Mater. 4(3/4), 128–137.
Bažant, Z. P. (1997). Scaling of quasibrittle fracture: Asymptotic analysis. Int. J. Fract. 83(1), 19–40.
Bažant, Z. P. (2001). Size effects in quasibrittle fracture: Apercu of recent results. In R., de Borst, J., Mazars, G., Pijaudier-Cabot, & J. G. M., van Mier (eds.), Fracture Mechanics of Concrete Structures (Proceedings of FraMCos-4 International Conference). A. A. Balkema, Lisse, pp. 651–658.
Bažant, Z. P. (2002a). Scaling of sea ice fracture – Part I: Vertical penetration. J. Appl. Mech. ASME 69, 11–18.
Bažant, Z. P. (2002b). Scaling of sea ice fracture – Part II: Horizontal load from moving ice. J. Appl. Mech. ASME 69, 19–24.
Bažant, Z. P. (2004a). Probability distribution of energetic-statistical size effect in quasibrittle fracture. Prob. Eng. Mech. 19(4), 307–319.
Bažant, Z. P. (2004b). Scaling theory of quaisbrittle structural failure. Proc. Nat. Acad. Sci. USA 101(37), 13400–13407.
Bažant, Z. P. (2005). Scaling of Structural Strength. 2nd edition. Elsevier, London.
Bažant, Z. P., & Becq-Giraudon, E. (2002). Statistical prediction of fracture parameters of concrete and implications for choice of testing standard. Cem. Concr. Res. 32(4), 529–556.
Bažant, Z. P., Belytschko, T., & Chang, T.-P. (1984). Continuum model for strain softening. J. Eng. Mech. ASCE 110(12), 1666–1692.
Bažant, Z. P., & Cedolin, L. (1979). Blunt crack band propagation in finite element analysis. J. Eng.Mech. Div. ASCE 105, 297–315.
Bažant, Z. P., & Cedolin, L. (1980). Fracture mechanics of reinforced concrete. J. Eng. Mech. Div. ASCE 106, 1257–1306.
Bažant, Z. P., & Cedolin, L. (1991). Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories. Oxford University Press, New York.
Bažant, Z. P., & Chen, E.-P. (1997). Scaling of structural failure. Appl. Mech. Rev. ASME 50(10), 593–627.
Bažant, Z. P., Daniel, I. M., & Li, Z. (1996). Size effect and fracture characteristics of composite laminates. J. Eng. Mater. Technol, ASME 118(3), 317–324.
Bažant, Z. P., & Frangopol, D. M. (2002). Size effect hidden in excessive load factor. J. Struct. Eng. ASCE 128(1), 80–86.
Bažant, Z. P., Gettu, R., & Kazemi, M. T. (1991). Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. Int. J. Rock Mech. Miner. Sci. 28(1), 43–51.
Bažant, Z. P., & Hubler, M. H. (2014). Theory of cyclic creep of concrete based on paris law for fatigue growth of subcritical microcracks. J. Mech. Phys. Solids 63, 187–200.
Bažant, Z. P., & Jirásek, M. (2002). Nonlocal integral formulations of plasticity and damage: Survey of progress. J. Eng. Mech. ASCE 128(11), 1119–1149.
Bažant, Z. P., & Kazemi, M. T. (1990a). Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete. Int. J. Fract. 44, 111–131.
Bažant, Z. P., & Kazemi, M. T. (1990b). Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length. J. Amer. Ceramic Soc. 73(7), 1841– 1853.
Bažant, Z. P., & Kazemi, M. T. (1991). Size effect on diagonal shear failure of beams without stirrups. ACI Struct. J. 88, 268–276.
Bažant, Z. P., & Kim, J.-J. (1998a). Size effect in penetration of sea ice plate with part-through cracks. I. Theory. J. Eng. Mech. ASCE 124(12), 1310–1315.
Bažant, Z. P., & Kim, J.-J. (1998b). Size effect in penetration of sea ice plate with part-through cracks. II. Results. J. Eng. Mech. ASCE 124(12), 1316–1324.
Bažant, Z. P., Kim, J.-J. II., Daniel, I. M., Becq-Giraudon, E., & Zi, G. (1999). Size effect on compression strength of fiber composites failing by kink band propagation. Int. J. Fract. 95, 103– 141.
Bažant, Z. P., Kim, K. T., & Yu, Q. (2013). Non-uniqueness of cohesive-crack stress-separation law of human and bovine bones and remedy by size effect tests. Int. J. Fract. 181, 67–81.
Bažant, Z. P., & Le, J.-L. (2009). Nano-mechanics based modeling of lifetime distribution of quasibrittle structures. J. Eng. Fail. Anal. 16, 2521–2529.
Bažant, Z. P., Le, J.-L., & Bazant, M. Z. (2009). Scaling of strength and lifetime distributions of quasibrittle structures based on atomistic fracture mechanics. Proc. Natl. Acad. Sci. USA 106, 11484–11489.
Bažant, Z. P., Le, J.-L., & Hoover, C. G. (2010). Nonlocal boundary layer model: Overcoming boundary condition problems in strength statistics and fracture analysis of quasibrittle materials. In Fracture Mechanics of Concrete and Concrete Structures – Recent Advances in Fracture Mechanics of Concrete. Jeju, Korea, pp. 135–143.
Bažant, Z. P., & Li, Y.-N. (1994). Penetration fracture of sea ice plate: Simplified analysis and size effect. J. Eng. Mech. ASCE 120(6), 1304–1321.
Bažant, Z. P., & Li, Y.-N. (1995a). Penetration fracture of sea ice plate. Int. J. Solids Struct. 32(3/4), 303–313.
Bažant, Z. P., & Li, Y.-N. (1997). Cohesive crack with rate-dependent opening and viscoelasticity: I. mathematical model and scaling. Int. J. Fract. 86(3), 247–265.
Bažant, Z. P., & Li, Z. (1995b). Modulus of rupture: Size effect due to fracture initiation in boundary layer. J. Struct. Eng. ASCE 121(4), 739–746.
Bažant, Z. P., & Li, Z. (1996). Zero-brittleness size-effect method for one-size fracture test of concrete. J. Eng. Mech. ASCE 122(5), 458–468.
Bažant, Z. P., & Lin, F.-B. (1988a). Nonlocal smeared cracking model for concrete fracture. J. Struct. Eng. ASCE 114(11), 2493–2510.
Bažant, Z. P., & Lin, F.-B. (1988b). Nonlocal yield limit degradation. Int. J. Numer. Methods Eng. 26, 1805–1823.
Bažant, Z. P., Lin, F.-B., & Lippmann, H. (1993). Fracture energy release and size effect in borehole breakout. Int. J. Num. Anal. Methods Geomech. 17, 1–14.
Bažant, Z. P., & Novák, D. (2000a). Energetic-statistical size effect in quasibrittle failure at crack initiation. ACI Mater. J. 97(3), 381–392.
Bažant, Z. P., & Novák, D. (2000b). Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. I. theory. J. Eng. Mech. ASCE 126(2), 166–174.
Bažant, Z. P., & Novák, D. (2000c). Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. II. application. J. Eng. Mech. ASCE 126(2), 175–185.
Bažant, Z. P., & Oh, B.-H. (1983). Crack band theory for fracture of concrete. Mater. Struct. 16, 155–177.
Bažant, Z. P., & Ožbolt, J. (1990). Nonlocal microplane model for fracture, damage, and size effect in structures. J. Eng. Mech. ASCE 116(11), 2485–2505.
Bažant, Z. P., & Pang, S. D. (2006). Mechanics based statistics of failure risk of quasibrittle structures and size effect on safety factors. Proc. Natl. Acad. Sci. USA 103, 9434–9439.
Bažant, Z. P., & Pang, S. D. (2007). Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture. J. Mech. Phys. Solids 55, 91–134.
Bažant, Z. P., Pang, S.-D., Vořrechovský, M., Novák, D., & Pukl, R. (2004). Statistical size effect in quasibrittle materials: Computation and extreme value theory. In V. C., Li, K., Leung, K. J., Willam, & S., Billington (eds.), Fracture Mechanics of Concrete Structures (Proceedings of FraMCoS-5, 5th International Conference), pp. 153–162.
Bažant, Z. P., & Pfeiffer, P. A. (1987). Determination of fracture energy from size effect and brittleness number. ACI Mater. J. 84, 463–480.
Bažant, Z. P., & Pijaudier-Cabot, G. (1988). Nonlocal continuum damage, localization instability and convergence. J. Appl. Mech. ASME 55, 287–293.
Bažant, Z. P., & Pijaudier-Cabot, G. (1989). Measurement of characteristic length of nonlocal continuum. J. Eng. Mech. ASCE 115(4), 755–767.
Bažant, Z. P., & Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boca Raton.
Bažant, Z. P., & Prat, P. C. (1988). Effect of temperature and humidity on fracture energy of concrete. ACI Mater. J. 85-M32, 262–271.
Bažant, Z. P., & Schell, W. F. (1993). Fatigue fracture of high-strength concrete and size effect. ACI Mater. J. 90(5), 472–478.
Bažant, Z. P., Tabbara, M. R., Kazemi, M. T., & Pijaudier-Cabot, G. (1990). Random particle model for fracture of aggregate or fiber composites. J. Eng. Mech. ASCE 116(8), 1686–1705.
Bažant, Z. P.,Vořrechovský, M., & Novák, D. (2007). Asymptotic prediction of energetic-statistical size effect from deterministic finite element solutions. J. Eng. Mech. ASCE 128, 153–162.
Bažant, Z. P., & Xi, Y. (1991). Statistical size effect in quasi-brittle structures: II. Nonlocal theory. J. Eng. Mech. ASCE 117(7), 2623–2640.
Bažant, Z. P.,& Xu, K. (1991). Size effect in fatigue fracture of concrete. ACIMater. J. 88(4), 390– 399.
Bažant, Z. P., & Yavari, A. (2005). Is the cause of size effect on structural strength fractal or energetic-statisticalř Eng. Fract. Mech. 72, 1–31.
Bažant, Z. P., & Yavari, A. (2007). Response to A. Carpinteri, B. Chiaia, P. Cornetti and S. Puzzi's comments on “Is the cause of size effect on structural strength fractal or energetic-statisticalř” Eng. Fract. Mech. 74, 2897–2910.
Bažant, Z. P., & Yu, Q. (2004). Size effect in concrete specimens and structures: New problems and progress. In V. C., Li, K. Y., Leung, K. J., Willam, & S. L., Billington (eds.), Fracture Mechanics of Concrete Structures, Proceedings of FraMCoS-5, 5th International Conference on Fracture Mechanics of Concrete and Concrete Structures, pp. 153–162.
Bažant, Z. P., & Yu, Q. (2006). Reliability, brittleness and fringe formulas in concrete design codes. J. Struct. Eng. ASCE 132(1), 3–12.
Bažant, Z. P., & Yu, Q. (2009). Universal size effect law and effect of crack depth on quasi-brittle structure strength. J. Eng. Mech. ASCE 135(2), 78–84.
Bažant, Z. P., & Yu, Q. (2011). Size effect testing of cohesive fracture parameters and nonuniqueness of work-of-fracture method. J. Eng. Mech. ASCE 137(8), 580–588.
Bažant, Z. P., Zhou, Y., Daniel, I. M., Caner, F. C., & Yu, Q. (2006). Size effect on strength of laminate-foam sandwich plates. J. Eng. Mater. Tech. ASME. 128(3), 366–374.
Bažant, Z. P., Zhou, Y., Novák, D., & Daniel, I. M. (2004). Size effect on flexural strength of fiber-composite laminate. J. Eng. Mater. Tech. ASME 126(1), 29–37.
Bažant, Z. P., Zhou, Y., Zi, G., & Daniel, I. M. (2003). Size effect and asymptotic matching analysis of fracture of closed-cell polymeric foam. Int. J. Solids Struct. 40, 7197–7217.
Bažant, Z. P., Zi, G., & McClung, D. (2003). Size effect law and fracture mechanics of the triggering of dry snow slab avalanches. J. Geophy. Res. 108(B2), 2119–2129.
Bazant, M. Z. (2000). The largest cluster in subcritical percolation. Phys. Rev. E 62, 1160–1669.
Bazant, M. Z. (2002). Stochastic renormalization group in percolation. Physica A 316, 451–477.
Bazant, M. Z., Choi, J., & Davidovitch, B. (2003). Dynamics of conformal maps for a class of non-Laplacian growth phenomena. Phys. Rev. Lett. 91, 045503.
Beale, P. D., & Duxbury, P. M. (1988). Theory of dielectric breakdown in metal-loaded dielectrics. Phys. Rev. B 40, 4641.
Becq-Giraudon, E. (2000). Size Effect on Fracture and Ductility of Concrete and Fiber Composites. PhD thesis, Northwestern University.
Bender, M. C., & Orszag, S. A. (1978). Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, New York.
Benjamin, J. R., & Cornell, C. A. (1970). Probability, Statistics, and Decisions for Civil Engineers. McGraw-Hill, New York.
Beremin, F. M. (1983). A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall. Trans. 114A, 2277–2287.
Bigleya, R. F., Gibelingb, J. C., Stoverc, S. M., Hazelwooda, S. J., Fyhriea, D. P., & Martin, R. B. (2007). Volume effects on fatigue life of equine cortical bone. J. Biomech. 40, 3548–3554.
Bogy, D. B. (1971). Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. ASME 38, 377–385.
Bolander, J. E., Hong, G. S., & Yoshitake, K. (2000). Structural concrete analysis using rigidbody- spring networks. J. Comput. Aided Civil Infrastruct. Eng. 15, 120–133.
Bolander, J. E., & Saito, S. (1998). Fracture analysis using spring network with random geometry. Eng. Fract. Mech. 61(5–6), 569–591.
Bolotin, V. V. (1969). Statistical Methods in Structural Mechanics. Holden-Day, San Francisco.
Borden, M. J., Hughes, T. J. R., Landis, C. M., & Verhoosel, C. V. (2014). A higher-order phasefield model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Comp. Methods Appl. Mech. Eng. 273, 100–118.
Borden, M. J., Verhoosel, C. V., Scott, M. A., Hughes, T. J. R., & Landis, C. M. (2012). A phasefield description of dynamic brittle fracture. Comp. Methods Appl. Mech. Eng. 217-220, 77–95.
Borino, G., Failla, B., & Parrinello, F. (2003). A symmetric nonlocal damage theory. Int. J. Solids Struct. 40, 3621–3645.
Bouchaud, J.-P., & Potters, M. (2000). Theory of Financial Risks: From Statistical Physics to Risk Management. Cambridge University Press, Cambridge.
Bowman, D. R., & Stroud, D. (1989). Model for dielectric breakdown in metal-insulator composites. Phys. Rev. B 40, 4641.
Breysse, D., & Fokwa, D. (1992). Influence of disorder of the fracture process of mortar, In Proceedings of the International Conference, Fracture Mechanics of Concrete Structures. London, pp. 536–541.
Broberg, K. B. (1999). Cracks and Fracture. Academic Press.
Broughton, J. Q., Abraham, F. F., Bernstein, N., & Kaxiras, E. (1999). Concurrent coupling of length scales: Methodology and application. Phys. Rev. B 60, 2391–2403.
Buckingham, E. (1914). On physically linear systems; illustration of the use of dimensional equations. Phys. Rev. Ser. 2 IV(4), 345–376.
Buckingham, E. (1915). Model experiments and the form of empirical equations. Trans. ASME 37, 263–296.
Bulmer, M. G. (1979). Principles of Statistics. Dover, New York.
Caner, F. C., & Bažant, Z. P. (2013). Microplane model M7 for plain concrete: I. Formulation. J. Eng. Mech., ASCE 139(12), 1712–1723.
Caner, F. C., Bažant, Z. P., Hoover, C. G., Waas, A. M., & Shahwan, K. (2011). Microplane model for fracturing damage of triaxially braided fiber-polymer composites. J. Eng. Mater. Tech. ASME 133, 021024–1 – 021024–12.
Cannone Falchetto, A., Le, J.-L., Turos, M. I., & Marasteanu, M. O. (2014). Indirect determination of size effect on strength of asphalt mixture at low temperatures. Mater. Struct. 47(1–2), 157– 169.
Carmeliet, J., & de Borst, R. (1995). Stochastic approaches for damage evolution in standard and non-standard continua. Int. J. Solids Struct. 32, 1149–1160.
Carpenter, W. C. (1984). Mode I and mode II stress intensities for plates with cracks of finite opening. Int. J. Fract. 26, 201–214.
Carpinteri, A. (1986). Mechanical Damage and Crack Growth in Concrete. Martinus Nijhoff– Kluwer, Dordrecht Boston.
Carpinteri, A. (1987). Stress-singularity and generalized fracture toughness at the vertex of reentrant corners. Eng. Fract. Mech. 26, 143–155.
Carpinteri, A. (1989). Decrease of apprent tensile and bending strength with specimen size: Two different explanations based on fracture mechanics. Int. J. Solids Struct. 25, 407–429.
Carpinteri, A. (1994). Fractal nature of materials microstructure and size effects on apparent material properties. Mech. Mater. 18, 89–101.
Carpinteri, A., Chiaia, B., & Ferro, G. (1995a). Multifractal scaling law: An extensive application to nominal strength size effect of concrete structures. Technical Report 50, Atti del Dipartimento di Ingegneria Strutturale, Politecnico de Torino.
Carpinteri, A., Chiaia, B., & Ferro, G. (1995b). Size effect on nominal tensile strength of concrete structures: Multifractality of material ligament and dimensional transition from order to disorder. Mater. Struct. 28, 311–317.
Castillo, E. (1988). Extreme Value Theory in Engineering. Academic Press, San Diego.
Červenka, J. (1998). Applied brittle analysis of concrete structures. In H., Mihashi & K., Rokugo (eds.), 3rd International Conference on Fracture Mechanics of Concrete Structures. Aedificatio Publishers, Freiburg, Germany, pp. 1–15.
Červenka, J., Bažant, Z. P., & Wierer, M. (2005). Equivalent localization element for crack band approach to mesh-sensitivity in microplane model. Int. J. Numer. Methods Eng. 62, 700–726.
Chakraborti, B. K., & Benguigui, L. G. (1997). Statistical Physics of Fracture and Breakdown in Disordered Solids. Clarendon Press, Oxford.
Charles, R. J. (1958a). Static fatigue of glass I. J. Appl. Phys. 29(11), 1549–1553.
Charles, R. J. (1958b). Static fatigue of glass II. J. Appl. Phys. 29(11), 1554–1560.
Chatterjee, S., Kuo, Y., Lu, J., Tewg, J.-Y., & Majhi, P. (2006). Electrical reliability aspects of HfO2 high-k gate dieletrics with TaN metal gate electrodes under constant voltage stress. Microelectron. Reliabil. 46, 69–76.
Chiao, C. C., Sherry, R. J., & Hetherington, N. W. (1977). Experimental verification of an accelerated test for predicting the lifetime of organic fiber composites. J. Comp. Mater. 11, 79–91.
Ciavarella, M., Paggi, M., & Carpinteri, A. (2008). One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth. J. Mech. Phys. Solids 56, 3461–3432.
Coffin, L. F. (1962). Low cycle fatigue–a review. Appl. Mater. Res. 1(3), 129–141.
Coleman, B. D. (1958a). On the strength of classical fibers and fiber bundles. J. Mech. Phys. Solids 7, 60–70.
Coleman, B. D. (1958b). The statistics and time dependent of mechanical breakdown in fibers. J. Appl. Phys. 29(6), 968–983.
Coleman, T. F., & Li., Y. (1994). On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds. Math. Program. 67(2), 189–224.
Coleman, T. F., & Li., Y. (1996). An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418–445.
Cornell, C. A. (1969). A probability-based structural code. J. Am. Concr. Inst. 66(12), 974–985.
Cundall, P. A. (1971). A computer model for simulating progressive large scale movements in blocky rock systems. In Proceedings of the International Symposium Rock Fracture, Vol. 1, Nancy, France, paper no. II–8.
Cundall, P. A., & Strack, O. (1979). A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65.
Cusatis, G., Bažant, Z. P., & Cedolin, L. (2003a). Confinement-shear lattice model for concrete damage in tension and compression: I. Theory. J. Eng. Mech. ASCE 129(12), 1439– 1448.
Cusatis, G., Bažant, Z. P., & Cedolin, L. (2003b). Confinement-shear lattice model for concrete damage in tension and compression: II. Computation and validation. J. Eng. Mech. ASCE 129(12), 1449–1458.
Cusatis, G., Pelessone, D., & Mencarelli, A. (2011). Lattice discrete particle model (LDPM) for failure behavior of concrete. I. Theory. Cem. Concr. Comp. 22, 881–890.
Cusatis, G., & Schauffert, E. A. (2009). Cohesive crack analysis of size effect. Eng. Fract. Mech. 76, 2163–2173.
Daniels, H. E. (1945). The statistical theory of the strength of bundles and threads. Proc. R. Soc. London A 183, 405–435.
Danzer, R., Lube, T., Supancic, P., & Damani, R. (2008). Fracture of ceramics. Adv. Eng. Mater. 10(4), 275–298.
Danzer, R., Supancic, P., Pascual, J., & Lube, T. (2007). Fractue statistics of ceramics – Weibull statistics and deviations from Weibull statistics. Eng. Fract. Mech. 74, 2919–2932.
da Vinci, L. (1500s). The Notebook of Leonardo da Vinci (1945), Edward McCurdy, London (p. 546); and Les Manuscrits de Léonard de Vinci, transl. in French by C., Ravaisson-Mollien, Institut de France (1881-91), Vol. 3.
Degraeve, R., Groeseneken, G., Bellens, R., Ogier, J. L., Depas, M., Roussel, P. J., & Maes, H. E. (1998). New insights in the relation between electron trap generation and the statistical properties of oxide breakdown. IEEE Trans. Electron Dev. 45(4), 904–911.
De Moivre, A. (1733). Paper reproduced in D. E., Smith: Source Book in Mathematics. McGraw- Hill, New York, 1929.
Dempsey, J. P., Adamson, R. M., & Mulmule, S. V. (1995). Large-scale in-situ fracture of ice. In F. H., Wittmann (ed.), Proceedings of the 2nd International Conference Fracture Mechanics of Concrete Structures (FraMCoS-2), Aedificatio Publishers, Freiburg, pp. 575–684.
Dempsey, J. P., Adamson, R. M., & Mulmule, S. V. (1999). Scale effect on the insitu tensile strength and failure of first-year sea ice at resolute, NWR. Int. J. Fract. 95, 347–366.
Department of National Defense of Canada (2007). Technical Airworthiness Manual (TAM). Technical Report Document no. C-05-005-001/AG-001, 530 pp.
Desmorat, R., & Leckie, F. A. (1998). Singularities in bimaterials: Parametric study of an isotropic/anisotropic joint. Eur. J. Mech. A: Solids 17, 33–52.
Diao, X., Mai, L. Y., & Mai, Y.-W. (1995). A statistical model of residual strength and fatigue life of composite laminates. Comp. Sci. Technol. 54, 329–336.
Dimov, I. T. (2008). Monte Carlo Methods for Applied Scientists. World Scientific, Singapore.
Dos Santos, C., Strecker, K., Piorino Neto, F., de Macedo Silva, O. M., Baldacum, S. A., & da Silva., C. R. M. (2003). Evaluation of the reliability of Si3N4-Al2O3-CTR2O3 ceramics through Weibull analysis. Mater. Res. 6(4), 463–467.
Duckett, K. (2005). Risk analysis and the acceptable probability of failure. Struct. Eng. 83(15), 25–26.
Duffaut, P. (2013). The traps behind the failure of Malpasset arch dam, France, in 1959. J. Rock Mech. Geotech. Eng. 5, 335–341.
Duffy, S. F., Janosik, L. A., Wereszczak, A. A., Suzuki, A., Lamon, J., & Thomas, D. J. (2003). Life prediction of structural components. In Progress in Ceramic Gas Turbine Development, Vol. 2. ASME Press, New York, pp. 553–607.
Dugdale, D. S. (1960). Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–108.
Dumin, D. J., Maddux, J. R., Scott, R. S., & Subramoniam, R. (1994). A model relating wearout to breakdown in thin oxides. IEEE Trans. Electron Dev. 41(9), 1570–1579.
Dunn, M. L., Hui, C. Y., Labossiere, P. E. W., & Lin, Y. Y. (2001). Small scale geometric and material features at geometric discontinuities and their role in fracture analysis. Int. J. Fract. 110(2), 101–121.
Dunn, M. L., Suwito, W., & Cunningham, S. J. (1996). Stress intensities at notch singularities. Eng. Fract. Mech. 57(4), 417–430.
Dunn, M. L., Suwito, W., & Cunningham, S. J. (1997). Fracture initiation at sharp notches: Correlation using critical stress intensities. Int. J. Solids Struct. 34(29), 3873–3883.
Eliáš, J., Vořrechovský, M., Skořcek, J., & Bažant, Z. P. (2015). Stochastic discrete meso-scale simulations of concrete fracture: Comparison to experimental data. Eng. Fract. Mech. 135(1), 1–16.
Elishakoff, I. (1983). Probabilistic Methods in the Theory of Structures. John Wiley & Sons, Toronto, Canada.
Ellingwood, B. R. (2006).Mitigating risk from abnormal loads and progressive collapse. J. Perfor. Constr. Fact. 20(4), 315–323.
Eringen, A. C. (1966). A unified theory of thermomechanical materials. Int. J. Eng. Sci. 4, 179–202.
Eringen, A. C. (1972). Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10, 425–425.
Eringen, A. C., & Edelen, D. G. B. (1972). On nonlocal elasticity. Int. J. Eng. Sci. 10, 233–248.
Evans, A. G. (1972). A method for evaluating the time-dependent failure characteristics of brittle materials – and its application to polycrystalline alumina. J. Mater. Sci. 7, 1173–1146.
Evans, A. G. (1974). Analysis of strength degradation after sustained loading. J. Am. Ceram. Soc. 57(9), 410–411.
Evans, A. G., & Fu, Y. (1984). The mechanical behavior of alumina. In Fracture in Ceramic Materials. Elsevier, Amsterdam, pp. 56–88.
Evans, R. H., & Marathe, M. S. (1968). Microcracking and stress-strain curves in concrete for tension. Mater. Struct. 1, 61–64.
Eyring, H. (1936). Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283–291.
Feller, W. (1957). Introduction to Probability Theory and Its Applications, 2nd edition, JohnWiley & Sons, New York.
Fett, T. (1991). A fracture-mechanical theory of subcritical crack growth in ceramics. Int. J. Fract. 54, 117–130.
Fett, T., & Munz, D. (1991). Static and cyclic fatigue of ceramic materials. In Ceramics Today – Tomorrow's Ceramics. Elsevier, Amsterdam, pp. 1827–1835.
Fett, T., & Munz, D. (1993). Difference between static and cyclic fatigue effects in alumina. J. Mater. Sci. Lett. 12, 352–354.
Fisher, R. A., & Tippett, L. H. C. (1928). Limiting form of the frequency distribution the largest and smallest number of a sample. Proc. Cambridge Philos. Soc. 24, 180–190.
Fréchet, M. (1927). Sur la loi de probailité de l'écart maximum. Ann. Soc. Polon. Math. (Cracow) 6, 93.
Freed, Y., & Banks-Sills, K. (2008). A new cohesive zone model for mixed mode interface fracture in bimaterials. Eng. Fract. Mech. 75, 4583–4593.
Freudenthal, A. M. (1956). Safety and probability of structural failure. ASCE Trans. 121, 1337–1397.
Freudenthal, A. M. (1968). Statistical approach to brittle fracture. In Fracture: An Advanced Treatise, Vol. 2. Academic Press. New York, pp. 591–619.
Freudenthal, A. M. (1981). Selected Papers by Alfred M. Freudenthal: Civil Engineering Classics. American Society of Civil Engineers, New York.
Freudenthal, A. M., Garrelts, J. M., & Shinozuka, M. (1966). The analysis of structural safety. J. Struct. Eng. Div. ASCE 92(ST1), 267–324.
Galilei, G. (1638). Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze. Elsevirii, Leiden.
Gauss, C. F. (1809). The Heavenly Bodies Moving about the Sun in Conic Sections. Reprint, Dover, New York, 1963.
Geers, M. G. D., Peerlings, R. H. J., Brekelmans, W. A.M., & de Borst, R. (2000). Phenomenological nonlocal approaches based on implicit gradient-enhanced damage. Acta Mechan. 144(1– 2), 1–15.
Gettu, R., Bažant, Z. P., & Karr, M. E. (1990). Fracture properties and brittleness of high-strength concrete. ACI Mater. J. 87, 608–618.
Ghidini, G., Brazzelli, D., Clementi, C., & Pellizzer, F. (1999). Charge trapping mechanism under dynamic stress and its effect on failure time. In Proceedings of the 37th Annual Reliability Physics Symposium. IEEE, San Diego.
Ghoniem, N.M., Busso, E. P., Kioussis, N., & Huang, H. (2003).Multiscale modeling of nanomechanics and micromechanics: An overview. Philos. Mag. 83(31–34), 3475–3528.
Glasstone, S., Laidler, K. J., & Eyring, H. (1941). The Theory of Rate Processes. McGraw-Hill, New York.
Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. 44, 423–453.
Gomez, F. J., & Elices, M. (2003). A fracture criterion for sharp V-notched samples. Int. J. Fract. 123(3–4), 163–175.
Graham-Brady, L. L., Arwade, S. R., Corr, D. J., Gutiérrez, M. A., Breysse, D., Grigoriu, M., & Zabara, N. (2006). Probability and materials: From nano- to macro-scale: A summary. Prob. Eng. Mech. 21, 193–199.
Grassl, P., & Bažant, Z. P. (2009). Random lattice-particle simulation of statistical size effect in quasi-brittle structures failing at crack initiation. J. Eng. Mech. ASCE 135(2), 85–92.
Grenestedt, J. L., & Hallstrom, S. (1997). Crack initiation from homogeneous and bimaterial corners. J. Appl. Mech. ASME 64, 811–818.
Griffith, A. A. (1921). The phenomenon of rupture in solids. Philos. Trans. 221A, 582–593.
Gross, B. (1996). Least squares best fit method for the three parameterWeibull distribution: Analysis of tensile and bend specimens with volume or surface flaw failure. NASA Technical Report TM-4721, 1–21.
Gumbel, E. J. (1958). Statistics of Extremes. Columbia University Press, New York.
Györgyi, G., Moloney, N. R., Ozogány, K., & Rácz, Z. (2008). Finite-size scaling in extreme statistics. Phys. Rev. Lett. 100, 210601.
Hahn, H. T., & Kim, R. Y. (1975). Proof testing of composite materials. J. Comp. Mater. 9, 297–311.
Haldar, A., & Mahadevan, S. (2000a). Probability, Reliability, and Statistical Methods in Engineering Design. John Wiley & Sons, New York.
Haldar, A., & Mahadevan, S. (2000b). Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley & Sons, New York.
Halpin, J. C., Johnson, T. A., & Waddoups, M. E. (1972). Kinetic fracture models and structural reliability. Int. J. Fract. Mech. 8, 465–466.
Harlow, D. G., & Phoenix, S. L. (1978a). The chain-of-bundles probability model for the strength of fibrous materials I: Analysis and conjectures. J. Comp. Mater. 12, 195–214.
Harlow, D. G., & Phoenix, S. L. (1978b). The chain-of-bundles probability model for the strength of fibrous materials II: A numerical study of convergence. J. Comp. Mater. 12, 314–334.
Harlow, D. G., Smith, R. L., & Taylor, H. M. (1983). Lower tail analysis of the distribution of the strength of load-sharing systems. J. Appl. Prob. 20, 358–367.
Hasofer, A. M., & Lind, N. C. (1974). Exact and invariant second moment code format. J. Eng. Mech. Div. ASCE 100(EM1), 111–121.
Hastings, M. B. (2001). Fractal to nonfractal phase transition in the dielectric breakdown model. Phys. Rev. Lett. 87, 175502.
Heilmann, H., Hilsdorf, H., & Finsterwalder, K. (1969). Festigkeit und Verformung von Beton unter Zugspannungen. Heft 203, Deutscher Ausschuss für Stahlabeton.
Hill, R. (1963). Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids 11, 357–362.
Hillerborg, A., Modéer, M., & Petersson, P. E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6, 773–782.
Hillig, W. B., & Charles, R. J. (1964). Surfaces, stress-dependent surface reaction, and strength. In V. F., Zackay (ed.) Proceedings of the 2nd Berkeley International Materials Conference. John Wiley and Sons, New York.
Hoover, C. G., & Bažant, Z. P. (2013). Comprehensive concrete fracture tests: Size effects of types 1 & 2, crack length effect and postpeak. Eng. Fract. Mech. 110, 281–289.
Hoover, C. G., & Bažant, Z. P. (2014a). Cohesive crack, size effect, crack band and work-offracture models compared to comprehensive concrete fracture tests. Int. J. Fract. 187(1), 133– 143.
Hoover, C. G., & Bažant, Z. P. (2014b). Comparison of the Hu-Duan boundary effect model to size-shape effect law for quasi-brittle fracture based on new comprehensive fracture tests. J. Eng. Mech. ASCE 140(3), 480–486.
Hoover, C. G., & Bažant, Z. P. (2014c). Universal size-shape effect law based on comprehensive concrete fracture tests. J. Eng. Mech. ASCE 140(3), 473–479.
Hoover, C. G., Bažant, Z. P., Vorel, J., Wendner, R., & Hubler, M. H. (2013). Comprehensive concrete fracture tests: Description and results. Eng. Fract. Mech. 114, 92–103.
Hoshide, T. (1995). Proof testing and subsequent fatigue characteristics in ceramics. In H., Kishimoto, T., Hoshide, & N., Okabe (eds.), Cyclic Fatigue in Ceramics. Elsevier and The Society of Materials Science, Japan, pp. 207–232.
Hrennikoff, A. (1941). Solution of problems of elasticity by the framework method. J. Appl.Mech. 12, 169–175.
Hudson, J. A., Brown, E. T., & Fairhurst, C. (1971). Optimizing the control of rock failure in servo-controlled laboratory tests. Rock Mech. 3, 217–224.
Hughes, B. P., & Chapman, G. P. (1966). The complete stress-strain curve for concrete in direct tension. RILEM Bull. (Paris) 30, 95–97.
Hutchinson, J.W., & Suo, Z. (1992).Mixed-mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191.
Ibnabdeljalil, M., & Phoenix, S. L. (1995). Creep rupture of brittle matrix composite reinforced with time dependent fibers: scalings and Monte Carlo simulations. J. Mech. Phys. Solids 43(6), 897–931.
Iguro, M., Shioya, T., Nojiri|Y., & Akiyama|H. (1985). Experimental studies on shear strength of large reinforced concrete beams under uniformly distributed load. Conc. Lib. Int. 5, 137–154.
Ironside, J. G., & Swain, M. V. (1998). Ceramics in dental restorations – A review and critical issues. J. Austral. Ceram. Soc. 34(2), 78–91.
Irwin, G. R. (1958). Fracture. In W., Flügge (ed.), Handbuch der Physik, Vol. VI. Springer-Verlag, Berlin, pp. 551–590.
Jirásek, M., & Bažant, Z. P. (1995a). Macroscopic fracture characteristics of random particle systems. Int. J. Fract. 69, 201–228.
Jirásek, M., & Bažant, Z. P. (1995b). Particle model for quasibrittle fracture and application to sea ice. J. Eng. Mech. ASCE 121, 1016–1025.
Kanninen, M. F., & Popelar, C. H. (1985). Advanced fracture mechanics. Oxford University Press, New York.
Kaplan, M. F. (1961). Crack propagation and the fracture concrete. ACI J. 58(11), 591–610.
Karihaloo, B. L., Abdalla, H. M., & Xiao, Q. Z. (2003). Size effect in concrete beams. Eng. Fract. Mech. 70(7–8), 979–993.
Kausch, H. H. (1978). Polymer Fracture, Springer-Verlag, Berlin Heidelberg, New York.
Kawai, T. (1978). New discrete element models and their application to seismic response analysis of structures. Nucl. Eng. Des. 48, 207–229.
Kawakubo, T. (1995). Fatigue crack growth mechanics in ceramics. In H., Kishimoto, T., Hoshide, & N., Okabe (eds.) Cyclic Fatigue in Ceramics. Elsevier and The Society of Materials Science, Japan, pp. 123–137.
Kaxiras, E. (2003). Atomic and Electronic Structure of Solids. Cambridge University Press, Cambridge.
Kesler, C. E., Naus, D. J., & Lott, J. L. (1972). Fracture mechanics – Its applicability to concrete. In Proceedings of International Conference on the Mechanical Behavior of Materials, Kyoto, Japan, pp. 113–124.
Kfouri, A. P., & Rice, J. R. (1977). Elastic-plastic separation energy rate for crack advance in finite growth steps. In D. M. R., Taplin (ed.), Fracture 1977 (Proceedings of the 4th International Conference on Fracture, ICF4), Vol. 1, University of Waterloo, Canada, pp. 43–59.
Khare, R., Mielke, S. L., Paci, J. T., Zhang, S. L., Ballarini, R., Schatz, G. C., & Belytschko, T. (2007). Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys. Rev. B 75(7), 075412.
Khare, R., Mielke, S. L., Schatz, G. C., & Belytschko, T. (2008). Multiscale coupling schemes spanning the quantum mechanical, atomistic forcefield, and continuum regimes. Comp. Methods Appl. Mech. Eng. 197, 3190–3202.
Kim, Y.-H., & Lee, J. C. (2004). Reliability characteristics of high-k dielectrics. Microelectron. Reliabil. 44, 183–193.
Kirane, K., & Bažant, Z. P. (2015a). Microplane damage model for fatigue of quasibrittle materials: Subcritical crack growth, lifetime and residual strength. Int. J. Fatigue 70, 93–105.
Kirane, K., & Bažant, Z. P. (2015b). Size effect in Paris law for quasibrittle materials analyzed by the microplane constitutive model M7.Mech. Res. Commune. 68, 627–631.
Kirchner, H. P., & Walker, R. E. (1971). Delayed fracture of alumina ceramics with compressive surface layers. Mater. Sci. Eng. 8, 301–309.
Kittl, P., & Diaz, G. (1988). Weibull's fracure statistics, or probabilistic strength of materials: State of the art. Res. Mechan. 24, 99–207.
Kittl, P., & Diaz, G. (1989). Some engineering applications of the probabilistic strength of materials. Appl. Mech. Rev. 42, 108–112.
Kittl, P., & Diaz, G. (1990). Size effect on fracture strength in the probabilistic strength of materials. Reliabil. Eng. Syst. Saf. 28, 9–21.
Knauss, W. C. (1973). On the steady propagation of a crack in a viscoelastc sheet; Experiment and analysis. In H. H., Kausch (ed.), The Deformation in Fracture of High Polymers. Plenum Press, New York, pp. 501–541.
Knauss, W. C. (1974). On the steady propagation of a crack in a viscoelastc plastic sold. J. Appl. Mechan. ASME 41, 234–248.
Knott, J. F. (1973). Fundamentals of Fracture Mechanics. Butterworth, London.
Kramers, H. A. (1941). Brownian motion in a field of force and the diffusion model of chemical reaction. Physica 7, 284–304.
Krausz, A. S., & Krausz, K. (1988). Fracture Kinetics of Crack Growth. Kluwer Academic, Dordrecht, the Netherlands.
Krayani, A., Pijaudier-Cabot, G., & Dufour, F. (2009). Boundary effect on weight function in nonlocal damage model. Eng. Fract. Mech. 76(14), 2217–2231.
Kröner, E. (1966). Continuum mechanics and range of atomic cohesion forces. In T., Yokobori, T., Kawasaki, & J., Swedlow (eds.), Proceedings of the 1st International Conference on Fracture. Japanese Society for Strength and Fracture of Materials. Sendai, Japan, p. 27.
Kröner, E. (1967). Elasticity theory of materials with long range cohesive forces. Int. J. Solids Struct. 3, 731–742.
Labossiere, P. E.W., Dunn, M. L., & Cunningham, S. J. (2002). Application of bimaterial interface corner failure mechanics to silicon/glass anodic bonds. J. Mech. Phys. Solids 50, 405–433.
Le, J.-L. (2011). General size effect on strength of bi-material quasibrittle structures. Int. J. Fract. 172, 151–160.
Le, J.-L. (2012). A finite weakest link model of lifetime distribution of high-k gate dielectrics under unipolar AC voltage stress. Microelectron. Reliabil. 52, 100–106.
Le, J.-L. (2015). Size effect on reliability indices and safety factors of quasibrittle structures. Struct. Saf. 52, 20–28.
Le, J.-L., Ballarini, R., & Zhu, Z. (2015). Modeling of probabilistic failure of polycrystalline silicon MEMS structures. J. Am. Ceram. Soc. 98(6), 1685–1697.
Le, J.-L., & Bažant, Z. P. (2009). Strength distribution of dental restorative ceramics: Finite weakest link model with zero threshold. Dent. Mater. 25(5), 641–648.
Le, J.-L., & Bažant, Z. P. (2011). Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: II. Fatigue crack growth, lifetime and scaling. J. Mech. Phys. Solids 59, 1322–1337.
Le, J.-L., & Bažant, Z. P. (2012). Scaling of static fracture of quasibrittle structures: Strength, lifetime and fracture kinetics. J. Appl. Mech. ASME 79, 031006.
Le, J.-L.,& Bažant, Z. P. (2014). A finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading. J. Math. Mech. Solids 19, 56–70.
Le, J.-L., Bažant, Z. P., & Bazant, M. Z. (2009). Crack growth law and its consequences on lifetime distributions of quasibrittle structures. J. Phys. D: Appl. Phys. 42, 214008.
Le, J.-L., Bažant, Z. P., & Bazant, M. Z. (2011). Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, crack growth, lifetime and scaling. J. Mech. Phys. Solids. 59, 1291–1321.
Le, J.-L., Bažant, Z. P., & Yu, Q. (2010). Scaling of strength of metal-composite joints: II. Interface fracture analysis. J. Appl. Mech. ASME 77, 011012.
Le, J.-L., Cannone Falchetto, A., & Marasteanu, M. O. (2013). Determination of strength distribution of quasibrittle structures from mean size effect analysis. Mech. Mater. 66, 79–87.
Le, J.-L., & Eliáš, J. (2016). A probabilistic crack band model for quasibrittle fracture. J. Appl. Mech. ASME 83(5), 051005.
Le, J.-L., Eliáš, J., & Bažant, Z. P. (2012). Computation of probability distribution of strength of quasibrittle structures failing at macro-crack initiation. J. Eng. Mech. ASCE 138(7), 888–899.
Le, J.-L.,Manning, J., & Labuz, J. F. (2014). Scaling of fatigue crack growth in a rock. Int. J. Rock Mech. Miner Sci. 72, 71–79.
Le, J.-L., Pieuchot, M., & Ballarini, R. (2014). Effect of stress singularity magnitude on scaling of strength of quasibrittle structures. J. Eng. Mech. ASCE 140(5), 04014011.
Le, J.-L., & Xue, B. (2013). Energetic-statistical size effect in fracture of bimaterial hybrid structures. Eng. Fract. Mech. 111, 106–115.
Lee, H. L., Park, S. E., & Hahn, B. S. (1995). Modeling of cyclic fatigue stress for life prediction of structural ceramics. J. Mater. Sci. 30, 2521–2525.
Lee, J., & Fenves, G. L. (1998). Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. ASCE 124(8), 892–900.
Lee, S. G., Ma, Y., Thimm, G. L., & Verstraeten, J. (2008). Product lifecycle management in aviation maintenance, repair and overhaul. Comput. Indust. 59, 296–303.
Leguillon, D. (2002). Strength or toughnessř A criterion for crack onset at a notch. Eur. J. Mech. A. Solids 21, 61–72.
Leicester, R. H. (1969). The size effect of notches. In Proceedings of the 2nd Australasian Conference on Mechanics of Structural Materials. Melbourne, pp. 4.1–4.20.
Lekhnitskii, S. G. (1963). Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco.
Lemaire, M. (2009). Structural Reliability. ISTE and John Wiley & Sons, London and Hokoken.
Lennard-Jones, J. E. (1924). On the determination of molecular fields II. From the equation of state of a gas. Proc. R. Soc. London A 106(738), 463–477.
Levy, M., & Salvadori, M. (1992). Why Buildings Fall Down. W. W. Norton, New York.
Li, X., & Marasteanu, M. O. (2006). Investigation of low temperature cracking in asphalt mixtures by acoustic emission. Road Mater. Pavement Des. 7/4, 491–512.
Li, Y.-N., & Bažant, Z. P. (1994). Penetration fracture of ice plate: 2D analysis and size effect. J. Eng. Mech. ASCE 120(7), 1481–1498.
Li, Y.-N., & Bažant, Z. P. (1997). Cohesive crack with rate-dependent opening and viscoelasticity: II. Numerical algorithm, behavior and size effect. Int. J. Fract. 86(3), 267–288.
Lin, Q., & Labuz, J. F. (2013). Fracture of sandstone characterized by digital image correlation. Int. J. Rock Mech. Miner Sci. 60, 235–245.
Liu, D., & Fleck, N. A. (1999). Scale effect in the initiation of cracking of a scarf joint. Int. J. Fract. 95, 66–88.
Liu, W. K., Karpov, E. G., & Park, H. S. (2005). Nano Mechanics and Materials: Theory, Multiscale Methods and Applications. John Wiley & Sons, West Sussex, UK.
Liu, X. H., Suo, Z., & Ma, Q. (1999). Split singularities: Stress field near the edge of silicon die on polymer substrate. Acta Mater. 47, 67–76.
Lohbauer, U., Petchelt, A., & Greil, P. (2002). Lifetime prediction of CAD/CAM dental ceramics. J. Biomed. Mater. Res. 63(6), 780–785.
Mahesh, S., & Phoenix, S. L. (2004). Lifetime distributions for unidirectional fibrous composites under creep-rupture loading. Int. J. Fract. 127, 303–360.
Malvar, J. L., & Warren, G. E. (1988). Fracture energy for three-point-bend tests on single-edgenotched beams. Exp. Mech. 28(3), 266–272.
Marder, M. (2004). Effect of atoms on brittle fracture. Int. J. Fract. 130, 517–555.
Mariotte, E. (1686). Traité du mouvement des eaux, posthumously edited by M. de la, Hire; Eng. transl. by J. T., Desvaguliers, London (1718), p. 249; also Marriotte's Collected Works, 2nd ed., The Hague (1740).
Marti, P. (1989). Size effect in double-punch tests on concrete cylinders. ACI Mater. J. 86, 597–601.
McKinney, K. R., & Rice, R. W. (1981). Specimen size effects in fracture toughness testing of heterogeous ceramics by the notch beam test. In S. W., Freiman, & S. R., Fuller (eds.), Fracture Mechanics Methods for Ceramics, Rocks and Concrete. ASTM Special Technical Publication No. 745. American Society for Testing Materials, Philadelphia, pp. 118–126.
McPherson, J. W., Khamankar, R. B., & Shanware, A. (2000). Complementary model for intrinsic time-dependent dielectric breakdown in SiO2 dielectrics. J. Appl. Phys. 88, 5351– 5359.
Melchers, R. E. (1987). Structural Reliability, Analysis & Prediction. John Wiley & Sons, New York.
Mihashi, H. (1983). Stochastic theory for fracture of concrete. In F. H., Wittmann (ed.), Fracture Mechanics of Concrete. Elsevier, Amsterdam, pp. 301–339.
Mihashi, H., & Izumi, M. (1977). Stochastic theory for concrete fracture. Cem. Concr. Res. 7, 411–422.
Mihashi, H., & Zaitsev, J. W. (1981). Statistical nature of crack propagation. In F. H., Wittmann (ed.), Report to RILEM TC50-FMC, Vol. Section 4-2.
Miyakawa, T., Ichiki, T., Mitsuhashi, J., Miyamoto, K., Tada, T., & Koyama, T. (2007). Study of time dependent dielectric breakdown distribution in ultrathin gate oxide. Jpn. J. Appl. Phys. 46(28), 691–692.
Morse, P. M. (1929). Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34, 57–64.
Mulmule, S. V., Dempsey, J. P., & Adamson, R. M. (1995). Large-scale in-situ ice fracture experiments–part II: Modeling efforts. In Ice Mechanics – 1995 (ASME Joint AppliedMechanics and Materials Summer Conference). ASME, New York.
Munz, D., & Fett, T. (1999). Ceramics:Mechanical Properties, Failure Behavior, Materials Selection. Springer-Verlag, Berlin.
Nallathambi, P. (1986). Fracture Behaviour of Plain Concretes. PhD thesis, University of New Castle, Callaghan, Australia.
Nielsen, L. F. (1996). Lifetime and residual strength of wood subjected to static and variable load. Technical Report R-6, Department of Structural Engineering and Materials, Technical University of Denmark.
Niemeyer, L., Pietronero, L., & Wiesmann, H. J. (1984). Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52, 1033–1036.
Nordic Committee for Building Structures (NKB) (1978). Recommendation for loading and safety regulations for structural design. Technical Report 36.
Ogawa, T. (1995). Fatigue crack growth of monolithic and composite ceramics. In H., Kishimoto, T., Hoshide, & N., Okabe (eds.), Cyclic Fatigue in Ceramics. Elsevier and The Society of Materials Science, Japan, pp. 167–188.
Okabe, N., & Hirata, H. (1995). High temperature fatigue properties for some types of SiC and Si3N4 and the unified strength estimation method. In H., Kishimoto, T., Hoshide, & N., Okabe (eds.), Cyclic Fatigue in Ceramics. Elsevier and The Society of Materials Science, Japan, pp. 245–276.
Omeltchenko, A., Yu, J., Kalia, R. K., & Vashishta, P. (1997). Crack front propagation and fracture in a graphite sheet: A molecular dynamics study on parallel computers. Phys. Rev. Lett. 78(11), 2148–2151.
Ortiz, M., & Pandolfi, A. (1999). Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis. Int. J. Numer. Methods Eng. 44(9), 1267–1282.
Palmer, A. C., & Rice, J. R. (1973). The growth of slip surfaces on the progressive failure of over-consolidates clay. Proc. R. Soc. London A. 332(527–548).
Pang, S.-D., Bažant, Z. P., & Le, J.-L. (2008). Statistics of strength of ceramics: Finite weakest link model and necessity of zero threshold. Int. J. Fract. 154, 131–145.
Paris, P. C., & Erdogan, F. (1963). A critical analysis of crack propagation law. J. Basic Eng. 85, 528–534.
Park, K., Paulino, G. H., & Roesler, J. R. (2009). A unified potential-based cohesive crack model for mixed-mode fracture. J. Mech. Phys. Solids 57(6), 891–908.
Park, S. E., & Lee, H. L. (1997). Prediction of static fatigue life of ceramics. J. Mater. Sci. Lett. 16, 1352–1353.
Peerlings, R. H. J., de Borst, R., Brekelmans, W. A. M., & de Vree, J. H. P. (1996). Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Methods Eng. 39(19), 3391– 3403.
Peerlings, R. H. J., Geers, M. G. D., de Borst, R., & Brekelmans, W. A. M. (2001). A critical comparison of nonlocal and gradient-enhanced softening continua. Int. J. Solids Struct. 38(44– 45), 7723–7746.
Peirce, F. T. (1926). Tensile tests of cotton yarns – V. The weakest link. J. Textile Inst. 17, 355– 368.
Petch, N. J. (1954). The cleavage strength of polycrystals. J. Iron Steel Inst. 174, 25–28.
Petersson, P. E. (1981). Crack growth and development of fracture zones in plain concrete and similar materials. Report TVBM-1006, Division of Building Materials, Lund Institute of Technology, Lund, Sweden.
Phillips, R. (2001). Crystals, Defects and Microstructures: Modeling Across Scales. Cambridge University Press, Cambridge.
Phoenix, S. L. (1978a). The asymptotic time to failure of a mechanical system of parallel members. SIAM J. Appl. Math. 34(2), 227–246.
Phoenix, S. L. (1978b). Stochastic strength and fatigue of fiber bundles. Int. J. Fract. 14(3), 327– 344.
Phoenix, S. L., Ibnabdeljalil, M., & Hui, C.-Y. (1997). Size effects in the distribution for strength of brittle matrix fibrous composites. Int. J. Solids Struct. 34(5), 545–568.
Phoenix, S. L., & Tierney, L.-J. (1983). A statistical model for the time dependent failure of unidirectional composite materials under local elastic load-sharing among fibers. Eng. Fract. Mech. 18(1), 193–215.
Pietronero, L., & Wiesmann, H. J. (1988). From physical dielectric breakdown to the stochastic fractal model. Z. Phys. B: Condensed Matter 70, 87–93.
Pietruszczak, S., & Mróz, Z. (1981). Finite element analysis of deformation of strain-softening materials. Int. J. Numer. Methods Eng. 17, 327–334.
Pijaudier-Cabot, G., & Bažant, Z. P. (1987). Nonlocal damage theory. J. Eng. Mech. ASCE 113(10), 1512–1533.
Planas, J., & Elices, M. (1988). Conceptual and experimental problems in the determination of the fracture energy of concrete. In Proceedings of International Workshop on “Fracture Toughness and Fracture Energy, Test Methods for Concrete and Rock.” Tohoku University, Sendai, Japan, pp. 203–212.
Planas, J., & Elices, M. (1989). Size effect in concrete structures: Mathematical approximation and experimental validation, In J., Mazars & Z. P., Bažant (eds.), Cracking and Damage, Strain Localization and Size Effect (Proceedings of France–U.S. Workshop). Elsevier, Amsterdam, pp. 462–476.
Qian, Z., & Akisanya, A. R. (1998). An experimental investigation of failure initiation in bonded joints. Acta Mater. 46, 4895–4904.
Rackwitz, R. (1976). Practical probabilistic approach to design. Bulletin No. 112, Comité European du Béton.
Rackwitz, R., & Fiessler, B. (1976). Note on discrete safety checking when using nonnormal stochastic models for basic variables. In Load Project Working Session, MIT, Cambridge, MA.
Rackwitz, R., & Fiessler, B. (1978). Structural reliability under combined random load sequences. Comp. Struct. 9(5), 484–494.
Redner, S. (2001). A Guide to First-Passage Processes. Cambridge University Press, Cambridge.
Reedy, E. D., Jr. (2000). Comparison between interface corner and interfacial fracture analysis of an adhesively-bonded butt joint. Int. J. Solids Struct. 37, 2429–2442.
Rezakhani, R., & Cusatis, G. (2016). Asymptotic expansion homogenization of discrete fine-scale models with rotational degrees of freedom for the simulation of quasi-brittle materials. J. Mech. Phys. Solids 88, 320–345.
Rice, J. R. (1967). Mechanics of crack tip deformation and extension by fatigue. In Fatigue Crack Propagation. Special Technical Publication 415. ASTM, Philadelphia, pp. 247–309.
Rice, J. R. (1968a). In Fracture, Mathematical analysis of the mechanics of fracture H., Liebowitz, ed., Vol. 2, Academic Press, 192–308.
Rice, J. R. (1968B). Path independent integral and approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. ASME 35, 379–386.
Rice, J. R. (1988). Elastic fracture mechanics concepts for interface cracks. J. Appl. Mech. ASME 55, 98–103.
RILEM TC 89-FMT (1990). Size effect method for determining fracture energy and process zone of concrete. Mater. Struct. 23, 461–465.
RILEM TC QFS (2005). Quasibrittle fracture scaling and size effect – Final report. Mater. Struct. 37, 547–568.
Rinne, H. (2009). The Weibull Distribution. A Handbook. CRC Press, Boca Raton, London/ New York.
Risken, H. (1989). The Fokker-Planck Equation. Springer-Verlag, Berlin.
Ritchie, R. O. (2005). Incomplete self-similarity and fatigue crack growth. Int. J. Fract. 132, 197– 203.
Ritchie, R. O., Knott, J. F., & Rice, J. R. (1973). On the relation between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids 21, 395–410.
Rocco, C. G. (1995). Size Dependence and Fracture Mechanisms in the Diagonal Compression Splitting Test. PhD thesis, Universidad Politecnica de Madrid.
Rüsch, H., & Hilsdorf, H. (1963). Deformation characteristics of concrete under axial tension. Voruntersuchungen bericht (preliminary report), Munich.
Sabnis, G. M., & Mirza, S. M. (1979). Size effect in model concretes. J. Struct. Eng. Div. ASCE 105(6), 1007–1020.
Sakai, T., & Fujitani, K. (1989). A statistical aspect on fatigue behavior of alumina ceramics in rotating bending. Eng. Fract. Mech. 32(4), 653–664.
Sakai, T., & Hoshide, T. (1995). Statistical aspect on fatigue fracture of structural ceramics under cyclic loads. In H., Kishimoto, T., Hoshide, & N., Okabe (eds.), Cyclic Fatigue in Ceramics. Elsevier and The Society of Materials Science, Japan, pp. 189–206.
Salem, J. A., Nemeth, N. N., Powers, L. P., & Choi, S. R. (1996). Reliability analysis of uniaxially ground brittle materials. J. Eng. Gas Turbines & Power 118, 863–871.
Salviato, M., Chau, V. T., Li, W., Bažant, Z. P., & Cusatis, G. (2016). Direct testing of gradual postpeak softening of fracture specimens of fiber composites stabilized by enhanced grip stiffness and mass. J. Appl. Mech. ASME, 83, 11103 (16 pp.).
Salviato, M., Kirane, K., & Bažant, Z. P. (2014). Statistical distribution and size effect of residual strength after a period of constant load. J. Mech. Phys. Solids 64, 440–454.
Schauffert, E. A., & Cusatis, G. (2011). Lattice discrete particle model for fiber-reinforced concrete. I: Theory. J. Eng. Mech. ASCE 138(7), 826–833.
Schauffert, E. A., Cusatis, G., Pelessone, D., O'Daniel, J. L., & Baylot, J. T. (2011). Lattice discrete particle model for fiber-reinforced concrete. II: Tensile fracture and multiaxial loading behavior. J. Eng. Mech. ASCE 138(7), 834–841.
Schlangen, E., & van Mier, J. G. M. (1992). Experimental and numerical analysis of micromechanisms of fracture of cement-based composites. Cem. Concr. Res. 14, 105–118.
Sedov, L. I. (1959). Similarity and Dimensional Methods in Mechanics. Academic Press, New York.
Seweryn, A. (1994). Brittle fracture criterion for structures with sharp notches. Eng. Fract. Mech. 47, 673–681.
Sglavo, V. M., & Green, D. J. (1995). Threshold stress intensity factor in soda-lime silicate glass by interrupted static fatigue test. J. Eur. Ceram. Soc. 16, 645–651.
Sglavo, V.M., & Renzi, S. (1999). Fatigue limit in borosilicate glasses by interrupted static fatigue test. Phys. Chem. Glasses 40(2), 79–84.
Shioya, T., & Akiyama, H. (1994). Application to design of size effect in reinforced concrete structures. In H., Mihashi, H., Okamura, & Z. P., Bažant (eds.), Size Effect in Concrete Structures. E & FN Spon, London, pp. 409–416.
Sinclair, G. B., Okajima, M., & Griffin, J. H. (1984). Path independent integrals for computing stress intensity factors at sharp notches in elastic plates. Int. J. Numer. Methods Eng. 20(6), 999–1008.
Smith, J., Cusatis, G., Pelessone, D., Landis, E., O'Daniel, J. L., & Baylot, J. (2014). Discrete modeling of ultra-high-performance concrete with application to projectile penetration. Int. J. Impact Eng. 65, 13–32.
Smith, R. L. (1982). The asymptotic distribution of the strength of a series-parallel system with equal load sharing. Ann. Probab. 10(1), 137–171.
Soong, T. T. (2004). Fundamentals of Probability and Statistics for Engineers. John Wiley & Sons, Hoboken, NJ.
Stanley, P., & Inanc, E. Y. (1985). Assessment of surface strength and bulk strength of a typical brittle material. In S., Eggwertz & N., Lind (eds.), Probabilistic Methods. I. The Mechanics of Solids and Structures. Springer-Verlag, Berlin, pp. 231–251.
Stathis, J. H. (1999). Percolation models for gate oxide breakdown. J. Appl. Phys. 86(10), 5757–5766.
Stillinger, F. H., & Weber, T. A. (1985). Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5256–5271.
Stroh, A. N. (1958). Dislocations and cracks in anisotropic elasticity. Philos. Mag. 3, 625–646.
Studarta, A. R., Filser, F., Kochera, P., & Gauckler, L. J. (2007). Fatigue of zirconia under cyclic loading in water and its implications for the design of dental bridges. Dent.Mater. 23, 106–114.
Studarta, A. R., Filser, F., Kochera, P., Lüthy, H., & Gauckler, L. J. (2007). Cyclic fatigue in water of veneer framework composites for all-ceramic dental bridges. Dent. Mater. 23, 177–185.
Suné, J. (2001). New physics-based analytic approach to the thin-oxide breakdown statistics. IEEE Trans. Electron Dev. Lett. 22(6), 296–298.
Suné, J., Placencia, I., Barniol, N., Farrés, E., Martín, F., & Aymerich, X. (1990). On the breakdown statistics of very thin sio2 films. Thin Solid Films 185, 347–362.
Suné, J., Tous, S., & Wu, E. Y. (2009). Analytical cell-based model for the breakdown statistics of multilayer insulator stacks. IEEE Trans. Electron Dev. Lett. 30(12), 1359–1361.
Suresh, S. (1998). Fatigue of Materials. Cambridge University Press, Cambridge.
Syroka-Korol, E., & Tejchman, J. (2014). Experimental investigation of size effect in reinforced concrete beams failing by shear. Eng. Struct. 58, 63–78.
Tadmor, E. B., & Miller, R. E. (2011). Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge University Press, Cambridge.
Tadmor, E. B., Ortiz, M., & Phillips, R. (1996). Quasicontinuum analysis of defects in solids. Philos. Mag. 73, 1529–1563.
Tang, T., Bažant, Z. P., Yang, S., & Zollinger, D. (1996). Variable-notch one-size test method for fracture energy and process zone length. Eng. Fract. Mech. 55(3), 383–404.
Tersoff, J. (1988). New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37, 6991.
Thomas, D. J., Verrilli, M., & Calomino, A. (2002). Stress-life behavior of a C/SiC composite in a low partial pressure of oxygen environment part III: Life prediction using probabilistic residual strength rupture model. In H.-T., Lin and M., Singh (eds.), Ceramic Engineering and Science Proceedings. The American Ceramic Society, Westerville, Vol. 23(3), pp. 453–460.
Thouless, M. D., Hsueh, C. H., & Evans, A. G. (1983). A damage model of creep crack growth in polycrystals. Acta Metall. 31(10), 1675–1687.
Timoshenko, S. P., & Goodier, J. N. (1951). Theory of Elasticity.McGraw-Hill, New York Toronto London.
Tinschert, J., Zwez, D., Marx, R., & Ausavice, K. J. (2000). Structural reliability of alumina-, feldspar-, leucite-, mica- and zirconia-based ceramics. J. Dent. 28, 529–535.
Tippett, L. H. C. (1925). On the extreme individuals and the range of samples. Biometrika p. 364.
Tobolsky, A., & Erying, H. (1943). Mechanical properties of polymeric materials. J. Chem. Phys. 11, 125–134.
Turner, C. H., Wang, T., & Burr, D. B. (2001). Shear strength and fatigue properties of human cortical bone determined from pure shear tests. Calcif. Tissue Int. 69, 373–378.
Turos, M. I., Cannone Falchetto, A., Tebaldi, G., & Marasteanu, M. O. (2012). Determining the flexural strength of asphalt mixtures using the bending beam rheometer. In A., Scarpas, N., Kringos, I., Al-Qadi, & A., Loizos (eds.), Proceedings of the 7th RILEM Conference on Cracking in Pavements. Springer, Netherlands, pp. 11–20.
van der Hofstad, R., & Redig, F. (2006). Maximal clusters in non-critical percolation and related models. J. Stat. Physics 122(4), 671–703.
Vanmarcke, E. (2010). Random Fields Analysis and Synthesis. World Scientific, Singapore.
var der Hofstad, R., & Redig, F. (2006). Maximal clusters in non-critical percolation and related models. J. Stat. Phys. 122, 671–703.
van Vliet, M. R., & van Mier, J. G. (2000). Experimental investigation of size effect in concrete and sandstone under uniaxial tension. Engineering Fracture Mechanics, 65(2–3): 165–188.
Vashy, A. (1892). Sur les lois de similitude en physique. Annales Telégraphiques. 19, 25–28.
von Mises, R. (1936). La distribution de la plus grande de n valeurs. Rev. Math. Union Interbalcanique 1, 1.
Vořrechovský, M., & Sadílek, V. (2008). Computational modeling of size effects in concrete specimens under uniaxial tension. Int. J. Fract. 154, 27–49.
Wagner, H. D. (1989). Stochastic concepts in the study of size effects in the mechanical strength of highly oriented polymeric materials. J. Polym. Sci. 27, 115–149.
Wagner, H. D., Schwartz, P., & Phoenix, S. L. (1986). Lifetime statistics for single Kevlar 49 filaments in creep-rupture. J. Polym. Sci. 21, 1868–1878.
Walraven, J. (1995). Size effects: Their nature and their recognition in building codes. Studi Ricerche (Politecnico di Milano) 16, 113–134.
Walsh, P. F. (1972). Fracture of plain concrete. Indian Concrete J. 46(11), 469–470, 476.
Walsh, P. F. (1976). Crack initiation in plain concrete. Mag. Concr. Res. 28, 37–41.
Wanger, H. D., Phoenix, S. L., & Schwartz, P. (1984). A study of statistical variability in the strength of single aramid filaments. J. Comp. Mater. 18, 312–338.
Wawersik, W., & Fairhurst, C. (1970). A study of brittle rock fracture in laboratory compression experiments. Int. J. Rock Mech. Miner. Sci. 7(5), 561–575.
Weertman, J. (1966). Rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocation distributed on a crack plane. Int. J. Fract. 2, 460–467.
Weibull, W. (1939). The phenomenon of rupture in solids. Proc. R. Sweden Inst. Engrg. Res. 153, 1–55.
Weibull, W. (1951). A statistical distribution function of wide applicability. J. Appl. Mech. ASME 153(18), 293–297.
Wiederhorn, S. M. (1967). Influence of water vapor on crack propagation in soda-lime glass. J. Am. Ceram. Soc. 50(8), 407–414.
Wiederhorn, S. M., & Bolz, L. H. (1970). Stress corrosion and static fatigue of glass. J. Am. Ceram. Soc. 53(10), 543–548.
Wilk, G. D., Wallace, R. M., & Anthony, J. M. (2001). High-k gate dielectrics: Current status and materials properties considerations. J. Appl. Phys. 89(10), 5243–5275.
Williams, M. L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 74, 526–528.
Williams, T., & Baxer, S. C. (2006). A framework for stochastic mechanics. Prob. Eng. Mech. 21(3), 247–255.
Wisnom, M. (1992). The relationship between tensile and flexural strength of unidirectional composite. J. Comp. Mater. 26, 1173–1180.
Witten, T. A., & Sander, L. M. (1981). Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403.
Wittmann, F. H., ed. (1995). Fracture Mechanics of Concrete Structures, Proceedings of Second International Conference. Aedificatio Publishers, Freiburg.
Wnuk, M. P. (1974). Quasi-static extension of a tensile crack contained in viscoelasto plastic solid. J. Appl. Mech. ASME 41, 234–248.
Xu, M., Tabarraei, A., Paci, J. T., Oswald, J., & Belytschko, T. (2012). A coupled quantum/ continuum mechanics study of graphene fracture. Int. J. Fract. 173(2), 163–173.
Xu, X. F. (2007). A multiscale stochastic finite element method on elliptic problems involving uncertainties. Comp. Methods Appl. Mech. Eng. 196, 2723–2736.
Yang, J. N. (1978). Fatigue and residual strength degradation for graphite/epoxy composites under tension-compression cyclic loadings. J. Comp. Mater. 12, 19–39.
Yang, J. N., & Liu, M. D. (1977). Residual strength degradation model and theory of periodic proof tests for graphite/epoxy laminates. J. Comp. Mater. 11, 176–202.
Yavuz, B. O., & Tessler, R. E. (1993). Threshold stress intensity for crack growth in silicon carbide ceramics. J. Am. Ceram. Soc. 76(4), 1017–1024.
Young, T. (1807). A Course of Lectures on Natural Philosophy and the Mechanical Arts, Vol. I. Joseph Johnson, St Paul's Church Yard, London, p. 144.
Yu, Q., Bažant, Z. P., Bayldon, J. M., Le, J.-L., Caner, F. C., Ng, W. H., & Waas, A. M. (2010). Scaling of strength of metal-composite joints: I. Experimental investigation. J. Appl. Mech. ASME 77, 011011.
Yu, Q., Bažant, Z. P., & Le, J.-L. (2013). Scaling of strength of metal-composite joints: III. Numerical simulation. J. Appl. Mech. ASME 80, 054593.
Yu, Q., Le, J.-L., Hubler, M. H., Wendner, R., Cusatis, G., Bažant, Z. P. (2016). Comparison of main models for size effect on shear strength of reinforced and prestressed concrete beams. Structural Concrete (fib), 17(5), 778–789.
Zaitsev, J. W., & Wittmann, F. H. (1974). A statistical approach to study the mechanical behavior of porous materials under multiaxial state of stress. In Proceedings of the 1973 Sympoisum on Mechanical Behavior of Materials. Kyoto, Japan, p. 705.
Zech, B., & Wittmann, F. H. (1977). A complex study on the reliability assessment of the containment of a pwr, Part II. probabilitic approach to describe the behavior of materials. In T. A., Jaeger & B. A., Boley (eds.), Transactions of the 4th International Conference on Structural Mechanics in Reactor Technology. Vol. H, J1/11, European Communities, Brussels, Belgium, pp. 1–14.
Zhurkov, S. N. (1965). Kinetic concept of the strength of solids. Int. J. Fract. Mech. 1(4), 311–323.
Zhurkov, S. N., & Korsukov, V. E. (1974). Atomic mechanism of fracture of solid polymer. J. Polym. Sci. 12(2), 385–398.
Zubelewicz, A., & Bažant, Z. P. (1987). Interface modeling of fracture in aggregate composites. J. Eng. Mech. ASCE 113(11), 1619–1630.