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

Filippo CagnettiRodica Toader — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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.

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

Filippo CagnettiRodica Toader — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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

Adjoint methods for obstacle problems and weakly coupled systems of PDE

Filippo CagnettiDiogo GomesHung Vinh Tran — 2013

ESAIM: Control, Optimisation and Calculus of Variations

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.

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