An elliptic approximation for phase separation in a fractured material

Kerrek Stinson; Solveig Wittig

An elliptic approximation for phase separation in a fractured material

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arxiv 2408.03776 v1 pith:KFHETBAS submitted 2024-08-07 math.AP

Kerrek Stinson , Solveig Wittig This is my paper · ORCID

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keywords energyapproximationmaterialphaseelasticfractureseparationambrosio-tortorelli-type

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We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries in the cracked region, providing a heuristic approximation of the interfacial energy in the current material configuration. Our primary result shows that the sharp energy may be recovered via Gamma-convergence from a modified Cahn-Hilliard energy coupled with an Ambrosio-Tortorelli-type approximation of the (linear) elastic and fracture energy.

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Compactness for $GSBV^p$ via concentration-compactness
math.AP 2025-01 conditional novelty 6.0 of 10

The authors prove a compactness theorem for GSBV^p functions, a class used in variational fracture models, by applying concentration-compactness to a range-space concentration function.

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