In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the $\Gamma$-convergence of re-scaled energies, the strong convergence of minimizers, the Euler-Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.
From Finite to Linear Elastic Fracture Mechanics by Scaling / M., Negri; Zanini, Chiara. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 50:(2014), pp. 525-548. [10.1007/s00526-013-0645-1]
From Finite to Linear Elastic Fracture Mechanics by Scaling
ZANINI, CHIARA
2014
Abstract
In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the $\Gamma$-convergence of re-scaled energies, the strong convergence of minimizers, the Euler-Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2508681
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