Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps

Cicalese, Marco; Focardi, Matteo; Zeppieri, Caterina Ida

doi:10.1007/s00332-021-09733-1

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J Nonlinear Sci

2021

DOI: 10.1007/s00332-021-09733-1

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Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps

Marco Cicalese

Matteo Focardi

Caterina Ida Zeppieri

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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Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy

Conti,

Focardi,

Iurlano

2024

Arch Rational Mech Anal

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We consider a family of vectorial models for cohesive fracture, which may incorporate $$\textrm{SO}(n)$$ 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 $$\Gamma $$ Γ -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.

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Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy

Conti,

Focardi,

Iurlano

2024

Arch Rational Mech Anal

View full text Add to dashboard Cite

show abstract

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Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps

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.

Cited by 1 publication

References 54 publications

Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy

Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy

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