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

2019/06/18 by Manuel Friedrich, Friedrich, Manuel
Computer Science · Engineering · #49J45 #70G75 #74R10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.1906.07817

openalex publication_date 2019/06/18 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

We consider a nonlinear, frame indifferent Griffith model for nonsimple\nbrittle materials where the elastic energy also depends on the second gradient\nof the deformations. In the framework of free discontinuity and gradient\ndiscontinuity problems, we prove existence of minimizers for boundary value\nproblems. We then pass to a small strain limit in terms of suitably rescaled\ndisplacement fields and show that the nonlinear energies can be identified with\na linear Griffith model in the sense of \Γ-convergence. This complements\nthe study in [Arch. Ration. Mech. Anal. 225 (2017), 425-467] by providing a\nlinearization result in arbitrary space dimensions.\n

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