Quasi-static crack propagation in brittle materials is modeled via the Ambrosio–Tortorelli approximation. The crack is modeled by a smooth phase-field, defined on the whole computational domain. Since the crack is confined to a thin layer, the employment of anisotropic adapted grids is shown to be a really effective tool in containing computational costs. We extend the anisotropic error analysis, applied to the classical Ambrosio–Tortorelli approximation by Artina et al., to the generalized Ambrosio–Tortorelli functional, where a unified framework for several elasticity laws is dealt with as well as a non-convex fracture energy can be accommodated. After deriving an anisotropic a posteriori error estimator, we devise an algorithm which alternates optimization and mesh adaptation. Both anti-plane and plane-strain configurations are numerically checked.

Anisotropic mesh adaptation for the generalized Ambrosio-Tortorelli functional with application to brittle fracture

Micheletti, Stefano;Perotto, Simona;Signorini, Marianna
2018-01-01

Abstract

Quasi-static crack propagation in brittle materials is modeled via the Ambrosio–Tortorelli approximation. The crack is modeled by a smooth phase-field, defined on the whole computational domain. Since the crack is confined to a thin layer, the employment of anisotropic adapted grids is shown to be a really effective tool in containing computational costs. We extend the anisotropic error analysis, applied to the classical Ambrosio–Tortorelli approximation by Artina et al., to the generalized Ambrosio–Tortorelli functional, where a unified framework for several elasticity laws is dealt with as well as a non-convex fracture energy can be accommodated. After deriving an anisotropic a posteriori error estimator, we devise an algorithm which alternates optimization and mesh adaptation. Both anti-plane and plane-strain configurations are numerically checked.
2018
A posteriori error estimator; Adaptive finite element method; Ambrosio-Tortorelli functional; Anisotropic mesh adaptation; Brittle fracture; Modeling and Simulation; Computational Theory and Mathematics; Computational Mathematics
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1051406
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 4
social impact