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

  • Received: 24 June 2019 Accepted: 15 September 2019 Published: 26 November 2019
  • 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.

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

    Related Papers:

  • 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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