Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials
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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 $��$-convergence. This complements the study in [Arch. Ration. Mech. Anal. 225 (2017), 425-467] by providing a linearization result in arbitrary space dimensions.
- University of Münster Germany
Nonsimple materials, T57-57.97, Applied mathematics. Quantitative methods, variational fracture model, minimizer existence, Existence of solutions of equilibrium problems in solid mechanics, function of bounded variation and deformation, nonsimple materials, brittle materials, γ-convergence, 74R10, 49J45, 70G75, Mathematics - Analysis of PDEs, free discontinuity problems, Brittle fracture, FOS: Mathematics, Energy minimization in equilibrium problems in solid mechanics, functions of bounded variation and deformation, gamma-convergence, griffith energies, PDEs in connection with mechanics of deformable solids, variational fracture, free discontinuity problem, Analysis of PDEs (math.AP)
Nonsimple materials, T57-57.97, Applied mathematics. Quantitative methods, variational fracture model, minimizer existence, Existence of solutions of equilibrium problems in solid mechanics, function of bounded variation and deformation, nonsimple materials, brittle materials, γ-convergence, 74R10, 49J45, 70G75, Mathematics - Analysis of PDEs, free discontinuity problems, Brittle fracture, FOS: Mathematics, Energy minimization in equilibrium problems in solid mechanics, functions of bounded variation and deformation, gamma-convergence, griffith energies, PDEs in connection with mechanics of deformable solids, variational fracture, free discontinuity problem, Analysis of PDEs (math.AP)
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