Griffith energies as small strain limit of nonlinear models for nonsimple brittle materialsy
Friedrich M (2020)
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 2
Pages Range: 75-100
Journal Issue: 1
DOI: 10.3934/mine.2020005
Abstract
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.
Authors with CRIS profile
Involved external institutions
Germany (DE)How to cite
APA:
Friedrich, M. (2020). Griffith energies as small strain limit of nonlinear models for nonsimple brittle materialsy. Mathematics in Engineering, 2(1), 75-100. https://doi.org/10.3934/mine.2020005
MLA:
Friedrich, Manuel. "Griffith energies as small strain limit of nonlinear models for nonsimple brittle materialsy." Mathematics in Engineering 2.1 (2020): 75-100.
BibTeX: Download