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

Marco Cicalese; Matteo Focardi; Caterina Ida Zeppieri

doi:10.1007/s00332-021-09733-1

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

Marco Cicalese, Matteo Focardi, Caterina Ida Zeppieri

Associate Professorship of Mathematical Continuum Mechanics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	78
Journal	Journal of Nonlinear Science
Volume	31
Issue number	5
DOIs	https://doi.org/10.1007/s00332-021-09733-1
State	Published - Oct 2021

Keywords

Brittle fracture
Elliptic approximation
Free-discontinuity problems
Geometric rigidity
Linearised elasticity
Phase-field models
Piecewise-rigid maps
Γ -convergence

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10.1007/s00332-021-09733-1

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title = "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.",

keywords = "Brittle fracture, Elliptic approximation, Free-discontinuity problems, Geometric rigidity, Linearised elasticity, Phase-field models, Piecewise-rigid maps, Γ -convergence",

author = "Marco Cicalese and Matteo Focardi and Zeppieri, {Caterina Ida}",

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AU - Cicalese, Marco

AU - Focardi, Matteo

AU - Zeppieri, Caterina Ida

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Y1 - 2021/10

N2 - 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.

AB - 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.

KW - Brittle fracture

KW - Elliptic approximation

KW - Free-discontinuity problems

KW - Geometric rigidity

KW - Linearised elasticity

KW - Phase-field models

KW - Piecewise-rigid maps

KW - Γ -convergence

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JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 5

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ER -

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

Abstract

Keywords

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