Griffith energies as small strain limit of nonlinear models for nonsimple brittle materialsy - Friedrich, Manuel (Mathematics in Engineering, 2020)
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.
CRIS-Team Scopus Importer:2021-10-21
Keywords: Brittle materials; Free discontinuity problems; Functions of bounded variation and deformation; Griffith energies; Nonsimple materials; Variational fracture; Γ-convergence