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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.

Decomposition Results for Functions with Bounded Variation

Gianni Dal MasoRodica Toader — 2008

Bollettino dell'Unione Matematica Italiana

Some decomposition results for functions with bounded variation are obtained by using Gagliardo's Theorem on the surjectivity of the trace operator from W 1 ; 1 ( Ω ) into L 1 ( Ω ) . More precisely, we prove that every BV function can be written as the sum of a BV function without jumps and a BV function without Cantor part. Alternatively, it can be written as the sum of a BV function without jumps and a purely singular BV function (i.e., a function whose gradient is singular with respect to the Lebesgue measure)....

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