Phase-field approximation of functionals defined on piecewise-rigid maps
Marco Cicalese, Matteo Focardi, Caterina Ida Zeppieri
TL;DR
This paper introduces a variational approximation method for brittle fracture energies in piecewise-rigid solids, applicable to both nonlinear and linearized elasticity models, advancing the mathematical modeling of fracture mechanics.
Contribution
It develops a new Ambrosio-Tortorelli type approximation for fracture energies in piecewise-rigid maps, encompassing nonlinear and linear elasticity cases.
Findings
Established a variational approximation framework for brittle fracture energies.
Unified treatment of nonlinear and linear elasticity in fracture modeling.
Potential for improved computational methods in fracture mechanics.
Abstract
We provide a variational approximation of Ambrosio-Tortorelli type for brittle fracture energies of piecewise-rigid solids. Our result covers both the case of geometrically nonlinear elasticity and that of linearised elasticity.
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