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- W1639673600 abstract "In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in (15). We consider the case of n-dimensional finite elasticity, for an arbitrary n � 1, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time. In this paper we present a new existence result for a variational model of quasistatic growth for brittle cracks introduced in (15) and based on Griffith's idea (see (16)) that the crack growth is determined by the competition between the elastic energy of the body and the work needed to produce a new crack, or extend an existing one. The main feature of this model is that the crack path is not prescribed, but is a result of energy balance. In order to obtain our existence theorems in any space dimension and for a general bulk energy, we introduce a mathematical formulation of the problem in a suitable space of functions which may exhibit jump discontinuities on sets of codimension one. We now describe the model in more detail. The reference configuration is a bounded open set of R n with Lipschitz boundary ∂ = ∂D ∪ ∂N, with ∂D ∩ ∂N = O. On the Dirichlet part ∂D of the boundary we prescribe the boundary deformation, while on the Neumann part ∂N we apply the surface forces. In our formulation, a crack is any rectifiable set contained in and with finite n − 1 dimensional Hausdorff measure. We assume that the work done to produce the crack can be written as" @default.
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- W1639673600 date "2004-01-16" @default.
- W1639673600 modified "2023-09-27" @default.
- W1639673600 title "Quasistatic crack growth in finite elasticity" @default.
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