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PreprintarXiv licencearXiv

Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture in antiplane shear deformations

  • Veronika Auer-Volkmann
  • Lisa Beck
  • Bernd Schmidt
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Abstract

We set up and investigate an approximation scheme for a variational theory of cohesive fracture in antiplane shear deformations. We consider a family of functionals acting on scalar valued functions in general dimensions depending on a small parameter 0 < ε ≪ 1 and on two fields: the elastic part of the displacement field and an eigendeformation field that describes the inelastic response of the material beyond the elastic regime. We measure the inelastic contributions of the latter in terms of a non-local energy functional. Our main result shows that, as ε → 0, the approximate functionals Γ-converge to a cohesive zone model.

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Cite

BibTeXRIS
BibTeX
@misc{auervolkmann2026eigendamage,
  title = {{Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture in antiplane shear deformations}},
  author = {Veronika Auer-Volkmann and Lisa Beck and Bernd Schmidt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29734},
  eprint = {2609.29734},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29734},
}
RIS
TY  - UNPB
TI  - Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture in antiplane shear deformations
AU  - Veronika Auer-Volkmann
AU  - Lisa Beck
AU  - Bernd Schmidt
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29734
UR  - https://arxiv.org/abs/2609.29734
AB  - We set up and investigate an approximation scheme for a variational theory of cohesive fracture in antiplane shear deformations. We consider a family of functionals acting on scalar valued functions in general dimensions depending on a small parameter 0 < ε ≪ 1 and on two fields: the elastic part of the displacement field and an eigendeformation field that describes the inelastic response of the material beyond the elastic regime. We measure the inelastic contributions of the latter in terms of a non-local energy functional. Our main result shows that, as ε → 0, the approximate functionals Γ-converge to a cohesive zone model.
ER  -