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.

We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\u03f5$-gradient flow of the energy functional, as the "viscosity" parameter $\u03f5$ tends to zero.

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.

Some decomposition results for functions with bounded variation are obtained by using Gagliardo's Theorem on the surjectivity of the trace operator from ${W}^{1;1}(\mathrm{\Omega})$ into ${L}^{1}(\partial \mathrm{\Omega})$. 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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