Displaying similar documents to “Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach”

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

Filippo Cagnetti, Rodica Toader (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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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, 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

Weighted energy-dissipation functionals for gradient flows

Alexander Mielke, Ulisse Stefanelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate a global-in-time variational approach to abstract evolution by means of the functionals proposed by Mielke and Ortiz [ (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications...