Some remarks on the viscous approximation of crack growth

DOI10.3934/dcdss.2013.6.131zbMath1263.74044OpenAlexW2051041782MaRDI QIDQ1942763

Giuliano Lazzaroni, Rodica Toader

Publication date: 14 March 2013

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2013.6.131

zbMATH Keywords

brittle fracturevanishing viscositystress intensity factorenergy release ratelocal minimizerscrack propagationvariational modelsfree-discontinuity problemsGriffith's criterionenergy derivative

Mathematics Subject Classification ID

Brittle fracture (74R10) Stress concentrations, singularities in solid mechanics (74G70) Energy minimization in equilibrium problems in solid mechanics (74G65) Methods involving semicontinuity and convergence; relaxation (49J45) Theoretical approximation in context of PDEs (35A35) Free boundary problems for PDEs (35R35) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (8)

Optimal control of a rate-independent evolution equation via viscous regularization ⋮ Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue ⋮ Rate-independent stochastic evolution equations: parametrized solutions ⋮ Energetic formulation for rate-independent processes: remarks on discontinuous evolutions with a simple example ⋮ Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish ⋮ Linearly constrained evolutions of critical points and an application to cohesive fractures ⋮ Quasistatic evolution in perfect plasticity as limit of dynamic processes ⋮ Crack growth by vanishing viscosity in planar elasticity

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