Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-28T06:15:15.751Z Has data issue: false hasContentIssue false

6 - Mechanical Behavior and Relation to Structural Parameters

Published online by Cambridge University Press:  15 September 2022

Catalin R. Picu
Catalin R. Picu
Affiliation:
Rensselaer Polytechnic Institute, New York
Get access

Summary

This chapter presents a comprehensive overview of the mechanical behavior of Network materials, with emphasis on the structure–properties relation. Crosslinked and non-crosslinked Network materials are discussed in separate sections. The behavior of crosslinked networks in tension, shear, compression, and multiaxial loading is described. The effects of fiber tortuosity, fiber alignment, crosslink compliance, network connectivity, and variability of fiber properties on network stiffness and nonlinear behavior are discussed in detail. The size effect on linear and nonlinear material properties is evaluated in relation with network parameters. Three types of nonlinear behavior are identified, corresponding to networks that stiffen or soften continuously during deformation, and networks with an approximately linear response. Numerous examples of each type are presented, including collagen networks, fibrin and actin gels, elastomers, paper, and nonwovens. The response of non-crosslinked athermal networks, such as fiber wads, is studied in compression and tension. The effect of entanglements in athermal networks is analyzed and a parallel drawn with the mechanics of thermoplastics.

Keywords

structure–properties relationnonlinear elasticityelastic–plastic behaviorstabilitycompressionmultiaxialnon-crosslinkedentanglementssize effectstiffening
Type
Chapter
Information
Network Materials
Structure and Properties
 , pp. 146 - 251
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alava, M. & Niskanen, K. (2006). The physics of paper. Rep. Prog. Phys. 69, 669–723.CrossRefGoogle Scholar
Alkhagen, M. & Toll, S. (2007). Micromechanics of a compressed fiber mass. J. Appl. Mech. 74, 723–731.CrossRefGoogle Scholar
Alkhagen, M. & Toll, S. (2009). The effect of fiber diameter distribution on the elasticity of a fiber mass. J. Appl. Mech. 76, 041014.CrossRefGoogle Scholar
Andrews, E. W., Gioux, G., Onck, P., & Gibson, L. J. (2001). Size effects in ductile cellular solids. Part 2: Experimental results. Int. J. Mech. Sci. 43, 701–713.CrossRefGoogle Scholar
Andrews, E. W., Sanders, W. & Gibson, L. J. (1999). Compressive and tensile behavior of aluminum foams. Mat. Sci. Eng. A 270, 113–124.CrossRefGoogle Scholar
Baljasov, P. D. (1976). Compression of textile fibers in mass and technology of textile manufacture. Legkaya promyshlennost, Moscow.Google Scholar
Ban, E., Barocas, V. B., Shephard, M. S. & Picu, R. C. (2016a). Effect of fiber crimp on the elasticity of random fiber networks with and without embedding matrices. J. Appl. Mech. 83, 041008.CrossRefGoogle ScholarPubMed
Ban, E., Barocas, V. B., Shephard, M. S. & Picu, R. C. (2016b). Softening in random networks of non-identical beams. J. Mech. Phys. Sol. 87, 38–50.CrossRefGoogle ScholarPubMed
Bancelin, S., Lynch, B., Bonod-Bidaud, C., et al. (2015). Ex-vivo multiscale quantitation of skin biomechanics in wild-type and genetically-modified mice using multiphoton microscopy. Sci. Rep. 5, 17635.CrossRefGoogle ScholarPubMed
Barbier, C., Dendievel, R. & Rodney, D. (2009). Role of friction in the mechanics of nonbonded fibrous materials. Phys. Rev. E 80, 016115.CrossRefGoogle ScholarPubMed
Baudequin, M., Ryschenkow, G. & Roux, S. (1999). Non-linear elastic behavior of light fibrous materials. Eur. Phys. J. B 12, 157–162.CrossRefGoogle Scholar
Beil, N. B. & Roberts, W. W. (2002). Modeling and computer simulation of the compressional behavior of fiber assemblies. Textile Res. J. 72, 341–351.CrossRefGoogle Scholar
Bernardi, L., Hopf, R., Ferrari, A., Ehret, A. E. & Mazza, E. (2017). On the large strain deformation behavior of silicone-based elastomers for biomedical applications. Poly. Testing 58, 189–198.CrossRefGoogle Scholar
Bircher, K., Ehret, A. E. & Mazza, E. (2016). Mechanical characteristic of bovine Glisson’s capsule as a model tissue for soft collagenous membranes. J. Biomech. Eng. 138, 081005.Google Scholar
Broedersz, C. P. & MacKintosh, F. C. (2012). Molecular motors stiffen non-affine semiflexible polymer networks. Soft Matter 7, 3186–3191.CrossRefGoogle Scholar
Broedersz, C. P., Sheinman, M. & MacKintosh, F. C. (2012). Filament-length-controlled elasticity in 3D fiber networks. Phys. Rev. Lett. 108, 078102.Google Scholar
Broedersz, C. P., Sheinman, M. & MacKintosh, F. C. (2014). Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995–1036.Google Scholar
Buxton, G. A. & Clarke, N. (2007). Bending to stretching transition in disordered networks. Phys. Rev. Lett. 98, 238103.Google Scholar
Calladine, C. R. (1978). Buckminster Fuller’s tensegrity structures and Clerk Maxwell’s rule for the construction of stiff frames. Int. J. Sol. Struct. 15, 161–172.Google Scholar
Candau, S., Peters, A. & Herz, J. (1981). Experimental evidence for trapped chain entanglements: Their influence on macroscopic behavior of networks. Polymer 22, 1504–1510.CrossRefGoogle Scholar
Carnaby, G. A. & Pan, N. (1989). Theory of the compression hysteresis of fibrous assemblies. Text. Res. J. 59 , 275–284.CrossRefGoogle Scholar
Chen, N., Koker, M. K. A., Uzun, S. & Silberstein, M. N. (2016). In-situ X-ray study of the deformation mechanisms of non-woven polypropylene. Int. J. Sol. Struct. 97–98, 200–208.CrossRefGoogle Scholar
Deogekar, S. & Picu, R. C. (2017). Structure–properties relation for random networks of fibers with noncircular cross-section. Phys. Rev. E 95, 033001.Google Scholar
Domaschke, S., Morel, A., Kaufmann, R., et al. (2020) Predicting the macroscopic response of electrospun membranes based on microstructure and single fiber properties. J. Mech. Beh. Biomed. Mater. 104, 103634.Google Scholar
Duling, R. R., Dupaix, R. B., Katsube, N. & Lannutti, J. (2008). Mechanical characterization of electrospun polycaprolactone (PCL): A potential scaffold for tissue engineering. J. Biomech. Eng. 130, 011006.Google Scholar
Durville, D. (2005). Numerical simulation of entangled materials mechanical properties. J. Mater. Sci. 40, 5941–5948.Google Scholar
El-Rahman, A. I. A. & Tucker III, C. L. (2013). Mechanics of random discontinuous long-fiber thermoplastics. Part II: Direct simulation of uniaxial compression. J. Rheol. 57, 1463–1489.Google Scholar
Erman, B. & Mark, J. E. (1989). Rubber-like elasticity. Ann. Rev. Phys. Chem. 40, 351–374.CrossRefGoogle Scholar
Erman, B. & Mark, J. E. (1997). Structure and properties of rubberlike networks. Oxford University Press, New York.Google Scholar
Feng, S., Thorpe, M. F. & Garboczi, E. (1985). Effective medium theory of percolation on central force elastic networks. Phys. Rev. B 31, 276–280.Google Scholar
Flory, P. (1971). Principles of polymer chemistry. Cornell University Press, Ithaca, NY.Google Scholar
Fontaine, F., Noel, C., Monnerie, L. & Erman, B. (1989). Stress–strain–swelling behavior of amorphous polymeric networks: Comparison of experimental data with theory. Macromolecules 22, 3352–3355.Google Scholar
Foteinopoulou, K., Karayannis, N. C., Mavrantzas, V. G. & Kroger, M. (2006). Primitive path identification and entanglement statistics in polymer melts: Results from direct topological analysis on atomistic polyethylene models. Macromolecules 39, 4207–4216.CrossRefGoogle Scholar
Fuller, R. B. (1976). Synergetics: Explorations in the geometry of thinking. Macmillan, New York.Google Scholar
Gao, J. & Weiner, J. H. (1994). Nature of stress on the atomic level in dense polymer systems. Science 266, 748–752.Google Scholar
Gardel, M. L., Shin, J. H., MacKintosh, F. C., et al. (2004). Elastic behavior of crosslinked and bundled actin networks. Science 304, 1301–1305.CrossRefGoogle ScholarPubMed
de Gennes, P. G. (1979). Scaling concepts in polymer physics. Cornell University Press, Ithaca, NY.Google Scholar
Gent, A. N. (ed.) (2012). Engineering with rubber. How to design rubber components, 3rd ed. Hanser Publishers, Munich.Google Scholar
Gibson, L. J. & Ashby, M. F. (1988). Cellular solids: Structure and properties. Pergamon Press, Tarrytown, NY.Google Scholar
Glüge, R. (2013). Generalized boundary conditions on representative volume elements and their use in determining the effective material properties. Comput. Mat. Sci. 79, 408–416.Google Scholar
Grishanov, S., Tausif, M. & Russell, S. J. (2012). Characterization of fiber entanglement in nonwoven fabrics based on knot theory. Comp. Sci. Technol. 72, 1331–1337.CrossRefGoogle Scholar
Gusev, A. A. (2019). Numerical estimates of the topological effect in the elasticity of Gaussian polymer networks and their exact theoretical description. Macromolecules 52, 3244–3251.CrossRefGoogle Scholar
Harley, B. A., Leung, J. H., Silva, E. C. C. M. & Gibson, L. J. (2007). Mechanical characterization of collagen-glycosaminoglycan scaffolds. Acta Biomater. 3, 463–474.Google Scholar
Head, D. A., Levine, A. J. & MacKintosh, F. C. (2003). Distinct regimes of elastic response and deformation modes of crosslinked cytoskeletal and semiflexible polymer networks. Phys. Rev. E 68, 061907.Google Scholar
Heussinger, C. & Frey, E. (2006). Floppy modes and nonaffine deformations in random fiber networks. Phys. Rev. Lett. 97, 105501.Google Scholar
Heussinger, C. & Frey, E. (2007). Role of architecture in the elastic response of semiflexible polymer and fiber networks. Phys. Rev. E 75, 011917.CrossRefGoogle ScholarPubMed
Heussinger, C., Schaeter, B. & Frey, E. (2007). Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E 76, 031906.Google Scholar
Horgan, C. O. & Murphy, J. G. (2017). Poynting and reverse Poynting effects in soft materials. Soft Matter 13, 4916–4923.CrossRefGoogle ScholarPubMed
Hossain, M. S., Bergstrom, P. & Uesaka, T. (2019). Uniaxial compression of 3D entangled fiber networks: Impacts of contact interactions. Model. Simul. Mater. Sci. Eng. 27, 015006.Google Scholar
Huang, C. Y., Stankiewicz, A., Ateshian, G. A. & Mow, V. C. (2005). Anisotropy, inhomogeneity and tension–compression nonlinearity of human glenohumeral cartilage in finite deformation. J. Biomech. 38, 799–809.Google Scholar
Huisman, E. M. & Lubensky, T. C. (2011). Internal stresses, normal modes and nonaffinity in three-dimensional biopolymer networks. Phys. Rev. Lett. 106, 088301.Google Scholar
Islam, M. R. & Picu, R. C. (2018). Effect of network architecture on the mechanical behavior of random fiber networks. J. Appl. Mech. 85, 081011.CrossRefGoogle Scholar
Islam, M. R., Tudryn, G., Bucinell, R., Schadler, L. & Picu, R. C. (2017). Morphology and mechanics of fungal mycelium. Sci. Rep. 7, 13070.Google Scholar
Janmey, P. A., Euteneuer, U., Traub, P. & Schliwa, M. (1991). Viscoelastic properties of vimentin compared with other filamentous biopolymer networks. J. Cell. Biol., 113, 155–160.Google Scholar
Janmey, P. A., McCormick, M. E., Rammensee, S., et al. (2007). Negative normal stress in semiflexible biopolymer gels, Nat. Mater. 6, 48–51.CrossRefGoogle ScholarPubMed
Jansen, K. A., Licup, A. J., Sharma, A., et al. (2018). The role of network architecture in collagen mechanics. Biophys. J. 114, 2665–2678.CrossRefGoogle ScholarPubMed
Jawerth, L. M. (2013). The mechanics of fibrin networks and their alterations by platelets. PhD thesis, Harvard University.Google Scholar
Jiang, G., Liu, C., Liu, X., et al. (2010). Network structure and compositional effects on the tensile mechanical properties of hydrophobic association hydrogels with high mechanical strength. Polymer 51, 1507–1515.CrossRefGoogle Scholar
Johnson, K. L. (1985). Contact mechanics. Cambridge University Press, Cambridge.Google Scholar
Kabla, A. & Mahadevan, L. (2006). Nonlinear mechanics of soft fibrous networks. J. R. Soc. Interface 4, 99–106.CrossRefGoogle Scholar
Kang, H., Wen, Q., Janmey, P. A., et al. (2009). Nonlinear elasticity of stiff filament networks: Strain stiffening, negative normal stress and filament alignment in fibrin gels. J. Phys. Chem. B 113, 3799–3805.CrossRefGoogle ScholarPubMed
Kasza, K. E., Koenderink, G. H., Lin, Y. C., et al. (2009). Nonlinear elasticity of stiff biopolymers connected by flexible linkers. Phys. Rev. E 79, 041928.CrossRefGoogle ScholarPubMed
Komori, T. & Itoh, M. (1991). A new approach to the theory of the compression of fiber assemblies. Text. Res. J. 61, 420–428.Google Scholar
Komori, T., Itoh, M. & Takaku, A. (1992). Model analysis of the compressibility of fiber assemblies. Text. Res. J. 62, 567–574.CrossRefGoogle Scholar
Kurniawan, N. A., van Kempen, T. H. S., Sonneveld, S., et al. (2017). Buffers strongly modulate fibrin self-assembly into fibrous networks. Langmuir 33, 6342–6352.Google Scholar
Kwon, H. J., Rogalsky, A. D., Kovalchick, C. & Ravichandran, G. (2010). Application of digital image correlation method to biogel. Poly. Eng. Sci. 50, 1585–1593.CrossRefGoogle Scholar
Lake, S. P. & Barocas, V. H. (2011). Mechanical and structural contribution of non-fibrillar matrix in uniaxial tension: A collagen–agarose co-gel model. Ann. Biomed. Eng., 39, 1891–1903.Google Scholar
Lang, M. (2018). Elasticity of phantom model networks with cyclic defects. ACS Macro Lett. 7, 536–539.Google Scholar
Larson, R. G. (1988). Constitutive equations for polymer melts and solutions. Butterworths, Stoneham, MA.Google Scholar
Larson, R. G. (1999). The structure and rheology of complex fluids. Oxford University Press, Oxford.Google Scholar
Licup, A. J., Munster, S., Sharma, A., et al. (2015). Stress controls the mechanics of collagen networks. Proc. Nat. Acad. Sci. 112, 9573–9578.CrossRefGoogle ScholarPubMed
Licup, A. J., Sharma, A. & MacKintosh, F. C. (2016). Elastic regimes of subisostatic athermal fiber networks. Phys. Rev. E 93, 021407.Google Scholar
Lin, T. S., Wang, R., Johnson, J. A. & Olsen, B. D. (2019). Revisiting the elasticity theory of Gaussian phantom networks. Macromolecules 52, 1685–1694.CrossRefGoogle Scholar
Lin, Y. C., Yao, N. Y., Broedersz, C. P., et al. (2010). Origins of elasticity in intermediate filament networks. Phys. Rev. Lett. 104, 058101.Google Scholar
Lindstrom, S. B., Vader, D. A., Kulachenko, A. & Weitz, D. A. (2010). Biopolymer network geometries: Characterization, regeneration and elastic properties. Phys. Rev. E 82, 051905.Google Scholar
Ma, Y. H., Zhu, H. X., Su, B., Hu, G. K. & Perks, R. (2018). The elasto-plastic behavior of 3D stochastic fiber networks with crosslinkers. J. Mech. Phys. Sol. 110, 155–172.Google Scholar
MacKintosh, F. C., Kas, J. & Janmey, P. A. (1995). Elasticity of semiflexible biopolymer networks. Phys. Rev. Lett. 24, 4425–4428.Google Scholar
Mao, R., Goutianos, S., Tu, W., et al. (2017). Comparison of fracture properties of cellulose nanopaper, printing paper and buckypaper. J. Mater. Sci. 52, 9508–9519.Google Scholar
Mark, J. E., Rahalkar, R. R. & Sullivan, J. L. (1979). Model networks of end-linked PDMS chains. III. Effect of the functionality of the cross links. J. Chem. Phys. 70, 1794–1797.Google Scholar
Masse, J. P., Salvo, L., Rodney, D., Brechet, Y. & Bouaziz, O. (2006). Influence of relative density on the architecture and mechanical behavior of a steel metallic wool. Scripta Mater. 54, 1379–1383.Google Scholar
Mauri, A., Ehret, A. E., Perrini, M., et al. (2015). Deformation mechanisms of human amnion: Quantitative studies based on second harmonic generation microscopy. J. Biomech. 48, 1606–1613.Google Scholar
Maxwell, J. C. (1864). On the calculation of the equilibrium and stiffness of frames. Phil. Mag. 27, 294–299.Google Scholar
Meng, F. & Terentjev, E. M. (2016). Nonlinear elasticity of semiflexible filament networks. Soft Matter 12, 6749–6756.Google Scholar
Meng, L., Arnoult, O., Smith, M. & Wnek, G. E. (2012). Electrospinning of in-situ crosslinked collagen nanofibers. J. Mater. Chem. 22, 19412.CrossRefGoogle Scholar
Merson, J. & Picu, R. C. (2020). Size effects in random fiber networks controlled by the use of generalized boundary conditions. Int. J. Sol. Struct. 206, 314–321.Google Scholar
Meunier, L., Chagnon, G., Favier, D., Orgeas, L. & Vacher, P. (2008). Mechanical experimental characterization and numerical modelling of an unfilled rubber. Poly. Testing 27, 765–777.Google Scholar
Mezeix, L., Bouvet, C., Huez, J. & Poquillon, D. (2009). Mechanical behavior of entangled fibers and entangled cross-linked fibers during compression. J. Mater. Sci. 44, 3652–3661.Google Scholar
Missel, A. R., Bai, M., Klug, W. S. & Levine, A. J. (2010). Affine–nonaffine transition in networks of nematically ordered semiflexible polymers. Phys. Rev. E 82, 041907.CrossRefGoogle ScholarPubMed
de Molina, P. M., Lad, S. & Helgeson, M. E. (2015). Heterogeneity and its influence on the properties of difunctional poly(ethylene glycol) hydrogels: Structure and mechanics. Macromolecules 48, 5402–5411.Google Scholar
Motte, S. & Kaufman, L. J. (2012). Strain stiffening in collagen I networks. Biopolymers 99, 35–46.CrossRefGoogle Scholar
Moyo, D., Anandjiwala, R. D. & Patnaik, A. (2016). Micromechanics of hydroentangled nonwoven fabrics. Textile Res. J. 87, 135–146.Google Scholar
Na, Y. H., Tanaka, Y., Kawauchi, Y., et al. (2006). Necking phenomenon in double network gels. Macromolecules 39, 4641–4645.Google Scholar
Neckar, B. (1997). Compression and packing density of fibrous assemblies. Textile Res. J. 67, 123–130.Google Scholar
Neckar, B. & Das, D. (2012). Theory of structure and mechanics of fibrous assemblies. Woodhead Publishing, New Delhi.Google Scholar
Negi, V. & Picu, R. C. (2021). Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction. Soft Matter 17, 10186–10197.CrossRefGoogle ScholarPubMed
Nishi, K., Fujii, K., Chung, U. I., Shibayama, M. & Sakai, T. (2017). Experimental observation of two features unexpected from the classical theories of rubber elasticity. Phys. Rev. Lett. 119, 267801.Google Scholar
Niskanen, K. (ed.) (1998). Paper physics. Tappi Press, Helsinki.Google Scholar
Niskanen, K. (ed.) (2012). Mechanics of paper products. De Gruyter, Berlin.Google Scholar
Oliver, W. C. and Pharr, G. M. (2004). Measurement of hardness and elastic modulus by instrumented indentation: advances in understanding and refinements to methodology. J. Mater. Res. 19, 3–20.Google Scholar
Oeser, R., Ewen, B., Richter, D. & Fargo, B. (1988). Dynamic fluctuation of crosslinks in a rubber: A neutron-spin-echo study. Phys. Rev. Lett. 60, 1041–1044.Google Scholar
Onck, P. R., Koeman, T., van Dillen, T. & van der Giessen, E. (2005). Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95, 178102.Google Scholar
Ostoja-Starzewski, M. & Stahl, D. C. (2000). Random fiber networks and special elastic orthotropy of paper. J. Elast. 60, 131–149.Google Scholar
Ovaska, M., Bertalan, Z., Miksic, A., et al. (2017). Deformation and fracture of echinoderm collagen networks. J. Mech. Beh. Biomed. Mater. 65, 42–52.Google Scholar
Oyen, M. L. (2014). Mechanical characterization of hydrogel materials. Int. Mater. Rev. 59, 44–59.Google Scholar
Patel, P. C. & Kothari, V. K. (2001). Effect of specimen size and strain rate on the tensile properties of heat-sealed and needlepunched nonwoven fabrics. Indian J. Fibr. Text. Res. 26, 409–413.Google Scholar
Perrini, M., Mauri, A., Ehret, A. E., et al. (2015). Mechanical and microstructural investigation of the cyclic behavior of human amnion. J. Biomech. Eng. 137, 061010.CrossRefGoogle ScholarPubMed
Picu, R. C., Deogekar, S. & Islam, M. R. (2018). Poisson’s contraction and fiber kinematics in tissue: Insight from collagen network simulations. J. Biomech. Eng. 140, 021002.Google Scholar
Picu, R. C. & Pavel, M. C. (2003). Scale invariance of the stress production mechanism in polymeric systems. Macromolecules 36, 9205–9215.CrossRefGoogle Scholar
Piechocka, I. K., van Oosten, A. S. G., Breuls, R. G. M. & Koenderink, G. H. (2011). Rheology of heterotypic collagen networks. Biomacromolecules 12, 2797–2805.Google Scholar
Poquillon, D., Viguier, B. & Andrieu, E. (2005). Experimental data about mechanical behavior during compression tests for various matter fibers. J. Mater. Sci. 40, 5963–5970.Google Scholar
Poynting, J. H. (1909). On pressure perpendicular to the shear planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc. R. Soc. London A 82, 546–559.Google Scholar
Puleo, G. L., Zulli, F., Piovanelli, M., et al. (2013). Mechanical and rheological behavior of pNIPAAM crosslinked macrohydrogel. React. Funct. Polym. 73, 1306–1318.Google Scholar
Räisänen, V. I., Alava, M. J., Nieminen, R. M. and Niskanen, K. J. (1996). Elastic–plastic behaviour in fibre networks. Nordic Pulp Paper Res. J. 11, 243–248.Google Scholar
Rault, J., Marchal, J., Judeinstein, P. & Albouy, P. A. (2006). Stress-induced crystallization and reinforcement in filled natural rubbers: 2H NMR study. Macromolecules 39, 8356–8368.Google Scholar
Rigdahl, M. & Hollmark, H. (1986). Network mechanics. In Paper structure and properties, Bristow, J. A. & Kolseth, P., eds. Marcel Dekker, New York, pp. 241–266.Google Scholar
Roberts, A. P. & Garboczi, E. J. (2002). Elastic properties of model random 3D open-cell solids. J. Mech. Phys. Sol. 50, 33–55.Google Scholar
Rodney, D., Gadot, B., Martinez, O. R., Rolland du Roscoat, S. & Orgeas, L. (2015). Reversible dilatancy in entangled single-wire materials. Nature Mat. 15, 72–77.CrossRefGoogle ScholarPubMed
Ronca, G. & Allegra, G. (1975). An approach to rubber elasticity with internal constraints. J. Chem. Phys. 63, 4990–4998.Google Scholar
Rubinstein, M. & Colby, R. H. (2003). Polymer physics. Oxford University Press, Oxford.Google Scholar
Rubinstein, M. & Helfand, E. (1985). Statistics of the entanglement of polymers: Concentration effects. J. Chem. Phys. 82, 2477–2483.Google Scholar
Ruland, A., Chen, X., Khansari, A., et al. (2018). A contactless approach for monitoring the mechanical properties of swollen hydrogels. Soft Matt. 14, 7228–7236.Google Scholar
Schofield, J. (1938). Research on wool felting. J. Textile Inst. 29, T239–T252.CrossRefGoogle Scholar
Schraad, M. W. & Harlow, F. H. (2006). A stochastic constitutive model for disordered cellular materials: Finite strain uniaxial compression. Int. J. Sol. Struct. 43, 3542–3568.Google Scholar
Seth, R. S. & Page, D. H. (1981). The stress–strain curve of paper. In The role of fundamental research in paper making: Transactions of the symposium held at Cambridge, September 1981, 2nd ed. (January 1, 1983). Mechanical Engineering Publications Limited, London, pp. 421–452.Google Scholar
Shahsavari, A. S. & Picu, R. C. (2013). Size effect on mechanical behavior of random fiber networks. Int. J. Sol. Struct. 50, 3332–3338.Google Scholar
Sharma, A., Licup, A. J., Rens, R., et al. (2016). Strain-driven criticality underlines non-linear mechanics of fibrous networks. Phys. Rev. E 94, 042407.Google Scholar
Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C. & Janmey, P. A. (2005). Nonlinear elasticity in biological gels. Nature 435, 191–194.Google Scholar
Subramanian, G. & Picu, R. C. (2011). Mechanics of three-dimensional, nonbonded random fiber networks. Phys. Rev. E 83, 056120.Google Scholar
Sun, T. L., Kurokawa, T., Kuroda, S., et al. (2013). Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity. Nature Mater. 12, 932–937.CrossRefGoogle ScholarPubMed
Swane, G. T. G., Smaje, L. H. & Bergel, D. H. (1989). Distensibility of single capillaries and venules in the rat and frog mesentery. Int. J. Microcirc. Clin. Exp. 8, 25–42.Google Scholar
Tharmann, R., Claessens, M. M. A. E. & Bausch, A. R. (2007). Viscoelasticity of isotropically cross-linked actin networks. Phys. Rev. Lett. 98, 088103.Google Scholar
Ting, T. C. T. & Chen, T. (2005). Poisson’s ratio for anisotropic elastic materials can have no bounds. Q. J. Mech. Appl. Math. 58, 73–82.Google Scholar
Toll, S. (1998). Packing mechanics of fiber reinforcements. Polym. Eng. Sci. 38, 1337–1350.Google Scholar
Toll, S. & Manson, J. A. E. (1995). The elastic compression of a fiber network. J. Appl. Mech. 62, 223–228.Google Scholar
Treloar, L. R. G. (1944). Stress–strain data for vulcanized rubber under various types of deformation. Trans. Faraday Soc. 40, 59–70.Google Scholar
Vader, D., Kabla, A., Weitz, D. & Mahadevan, L. (2009). Strain-induced alignment in collagen gels. PLoS ONE 4, e5902.Google Scholar
Vasiliev, V. G., Rogovina, L. Z. & Slonimsky, G. L. (1985). Dependence of properties of swollen and dry polymer networks on the conditions of their formation in solution. Polymer 26, 1667–1676.Google Scholar
Verhille, G., Moulinet, S., Vandenberghe, N., Adda-Bedia, M., & LeGal, P. (2017). Structure and mechanics of aegagropilae fiber network. Proc. Nat. Acad. Sci. 114, 4607–4612.Google Scholar
Ward, I. M. & Sweeney, J. (2013). Mechanical properties of solid polymers, 3rd ed. Wiley, Chichester, UK.Google Scholar
Welling, L. W., Zupka, M. T. & Welling, D. J. (1995). Mechanical properties of basement membrane. Physiology 10, 30–35.Google Scholar
Wilhelm, J. & Frey, E. (2003). Elasticity of stiff polymer networks. Phys. Rev. Lett. 91, 108103.Google Scholar
Wong, D., Andriyana, A., Ang, B. C., et al. (2019). Poisson’s ratio and volume change accompanying deformation of randomly oriented electrospun nanofibrous membranes. Plast. Rubber Comp. 48, 456–465.CrossRefGoogle Scholar
van Wyk, C. M. (1946). Note on the compressibility of wool. J. Textile Inst. 37, T285–T292.Google Scholar
Yohsuke, B., Urayama, K., Takigawa, T. & Ito, K. (2011). Biaxial strain testing of extremely soft polymer gels. Soft Matter 7, 2632–2638.Google Scholar
Zagar, G., Onck, P. R., & van der Giessen, E. (2011). Elasticity of rigidly cross-linked networks of athermal filaments. Macromolecules 44, 7026–7033.Google Scholar
Zagar, G., Onck, P. R. & van der Giessen, E. (2015). Two fundamental mechanisms govern the stiffening of crosslinked networks. Biophys. J. 108, 1470–1479.Google Scholar
Zhang, M., Chen, Y., Chiang, F. P., Gouma, P. I. & Wang, L. (2019). Modeling the large deformation and microstructure evolution of nonwoven polymer fiber networks. J. Appl. Mech. 86, 011010.Google Scholar
Zhu, H. X., Hobdell, J. R. & Windle, A. H. (2000). Effects of cell irregularity on the elastic properties of open-cell foams. Acta Mater. 48, 4893–4900.Google Scholar
Zrinyi, M. & Horkay, F. (1987). On the elastic modulus of swollen gels. Polymer 28, 1139–1143.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×