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Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations
Author(s) -
Thomas Marita,
Bilgen Carola,
Weinberg Kerstin
Publication year - 2018
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201730004
Subject(s) - fracture (geology) , dissipation , brittle fracture , phase field models , field (mathematics) , phase (matter) , tensor (intrinsic definition) , cauchy distribution , mathematics , mechanics , materials science , mathematical analysis , physics , geometry , pure mathematics , thermodynamics , composite material , quantum mechanics
We present recent results on the mathematical analysis of phase‐field model for anisotropic fracture at finite strains. It is based on a modification of the Ambrosio‐Tortorelli model, formulated for polyconvex energy densities in terms of the modified invariants of the right Cauchy‐Green strain tensor and augmented by a viscous dissipation for the phase‐field variable. A suitable notion of solution is introduced and used for the simulation of a conchoidal fracture in a brittle specimen.