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Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials

Applied Mathematics Münster, University of Münster, Einsteinstrasse 62, 48149 Münster, Germany

This contribution is part of the Special Issue: Variational Models in Elasticity
Guest Editors: Lucia De Luca; Marcello Ponsiglione
Link: https://www.aimspress.com/newsinfo/1369.html

Special Issues: Variational Models in Elasticity

We consider a nonlinear, frame indifferent Griffith model for nonsimple brittle materials where the elastic energy also depends on the second gradient of the deformations. In the framework of free discontinuity and gradient discontinuity problems, we prove existence of minimizers for boundary value problems. We then pass to a small strain limit in terms of suitably rescaled displacement fields and show that the nonlinear energies can be identified with a linear Griffith model in the sense of Γ-convergence. This complements the study in [39] by providing a linearization result in arbitrary space dimensions.
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Keywords brittle materials; variational fracture; nonsimple materials; free discontinuity problems; Griffith energies; Γ-convergence; functions of bounded variation and deformation

Citation: Manuel Friedrich. Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials. Mathematics in Engineering, 2020, 2(1): 75-100. doi: 10.3934/mine.2020005

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This article has been cited by

  • 1. L. De Luca, M. Ponsiglione, Variational models in elasticity, Mathematics in Engineering, 2021, 3, 2, 1, 10.3934/mine.2021015

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