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A variational model for fracture mechanics: Numerical experiments. (English) Zbl 1166.74413
Summary: In the variational model for brittle fracture proposed by G. A. Francfort and J.-J. Marigo [J. Mech. Phys. Solids 46, No. 8, 1319–1342 (1998; Zbl 0966.74060)], the minimum problem is formulated as a free discontinuity problem for the energy functional of a linear elastic body. A family of approximating regularized problems is then defined, each of which can be solved numerically by a finite element procedure. Here we re-formulate the minimum problem within the context of finite elasticity. The main change is the introduction of the dependence of the strain energy density on the determinant of the deformation gradient. This change requires new, more general existence and \(\varGamma \)-convergence results. The results of some two-dimensional numerical simulations are presented, and compared with corresponding simulations made in [B. Bourdin, G. A. Francfort and J.-J. Marigo, J. Mech. Phys. Solids 48, No. 4, 797–826 (2000; Zbl 0995.74057)] for the linear elastic model.

MSC:
74R10 Brittle fracture
74G65 Energy minimization in equilibrium problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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