Published Paper

Inserted: 13 may 2022
Last Updated: 25 apr 2024

Journal: Archive for Rational Mechanics and Analysis
Volume: 248
Number: 21
Pages: 1-60
Year: 2022
Doi: 10.1007/s00205-024-01962-4
Links: link to open access

Abstract:

We consider a family of vectorial models for cohesive fracture, which may incorporate $\mathrm{SO}(n)$-invariance. The deformation belongs to the space of generalized functions of bounded variation and the energy contains an (elastic) volume energy, an opening-dependent jump energy concentrated on the fractured surface, and a Cantor part representing diffuse damage. We show that this type of functional can be naturally obtained as $\Gamma$-limit of an appropriate phase-field model. The energy densities entering the limiting functional can be expressed, in a partially implicit way, in terms of those appearing in the phase-field approximation.

Keywords: phase-field, cohesive fracture energy

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