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Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

Published online by Cambridge University Press:  09 October 2009

Filippo Cagnetti
Affiliation:
SISSA, via Beirut 2, 34014 Trieste, Italy. cagnetti@sissa.it
Rodica Toader
Affiliation:
Univ. Udine, Dip. Ingegneria Civile, via delle Scienze 208, 33100 Udine, Italy. toader@uniud.it
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Abstract

A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2009

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References

Barenblatt, G.I., The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7 (1962) 55129. CrossRef
Cagnetti, F., A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path. Math. Models Methods Appl. Sci. 18 (2008) 10271071. CrossRef
D.L. Cohn, Measure theory. Reprint of the 1980 original, Birkhäuser, Boston, USA (1993).
Dal Maso, G. and Toader, R., A model for the quasi-static growth of brittle fractures: existence and approximation results. Arch. Ration. Mech. Anal. 162 (2002) 101135. CrossRef
Dal Maso, G. and Zanini, C., Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. Roy. Soc. Edinburgh Sect. A 137 (2007) 253279. CrossRef
Dal Maso, G., Francfort, G.A. and Toader, R., Quasistatic crack growth in nonlinear elasticity. Arch. Ration. Mech. Anal. 176 (2005) 165225. CrossRef
Francfort, G.A. and Marigo, J.-J., Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 13191342. CrossRef
A. Mielke, Evolution of rate-independent systems, in Handbook of differential equations, evolutionary equations 2, C.M. Dafermos and E. Feireisl Eds., Elsevier, Amsterdam, The Netherlands (2005) 461–559.
J. Neveu, Discrete-Parameter Martingales. American Elsevier, Amsterdam, The Netherlands (1975).
M. Valadier, Young measures, in Methods of nonconvex analysis (Varenna, 1989) 1446, Lect. Notes Math., Springer, Berlin, Germany (1990) 152–188.

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