Phase-field approximation of functionals defined on piecewise-rigid maps
Analysis of PDEs
2021-08-18 v1
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.
Cite
@article{arxiv.2104.00658,
title = {Phase-field approximation of functionals defined on piecewise-rigid maps},
author = {Marco Cicalese and Matteo Focardi and Caterina Ida Zeppieri},
journal= {arXiv preprint arXiv:2104.00658},
year = {2021}
}
Related papers
View all related →
Analysis of PDEs · Mathematics
Phase-field approximation for a class of cohesive fracture energies with an activation threshold
Antonin Chambolle, Vito Crismale
2019-02-19
Analysis of PDEs · Mathematics
Convergence of critical points for a phase-field approximation of 1D cohesive fracture energies
Marco Bonacini, Flaviana Iurlano
2024-08-05
Analysis of PDEs · Mathematics
An elliptic approximation for phase separation in a fractured material
Kerrek Stinson, Solveig Wittig
2024-08-08
Numerical Analysis · Mathematics
Adaptive finite element convergence analysis of AT1 phase-field model for quasi-static fracture in strain-limiting solids
Ram Manohar, S. M. Mallikarjunaiah
2025-07-02
Analysis of PDEs · Mathematics
A derivation of Griffith functionals from discrete finite-difference models
Vito Crismale, Giovanni Scilla, Francesco Solombrino
2020-07-31
Analysis of PDEs · Mathematics
Ambrosio-Tortorelli Approximation of Quasi-Static Evolution of Brittle Fractures
Alessandro Giacomini
2007-05-23
Analysis of PDEs · Mathematics
Phase-field modelling of cohesive fracture. Part I: $\Gamma$-convergence results
Roberto Alessi, Francesco Colasanto, Matteo Focardi
2025-10-13
Applied Physics · Physics
Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface
Francesco Vicentini, Jonas Heinzmann, Pietro Carrara, Laura De Lorenzis
2026-01-06
Numerical Analysis · Mathematics
A micromorphic phase-field model for brittle and quasi-brittle fracture
Ritukesh Bharali, Fredrik Larsson, Ralf Jänicke
2022-06-24
Analysis of PDEs · Mathematics
A derivation of linearized Griffith energies from nonlinear models
Manuel Friedrich
2017-02-10
Numerical Analysis · Mathematics
An \textsf{AT1} phase-field framework for quasi-static anti-plane shear fracture: Unifying $\xi$-based adaptivity and nonlinear strain energy density function
Maria P. Fernando, S. M. Mallikarjunaiah
2025-07-01
Analysis of PDEs · Mathematics
Approximation of fracture energies with $p$-growth via piecewise affine finite elements
Sergio Conti, Matteo Focardi, Flaviana Iurlano
2019-12-13
Numerical Analysis · Mathematics
Selection of the Regularization Parameter in the Ambrosio-Tortorelli Approximation of the Mumford-Shah Functional for Image Segmentation
Yufei Yu, Weizhang Huang
2020-04-20
Analysis of PDEs · Mathematics
Gradient damage models for heterogeneous materials
Annika Bach, Teresa Esposito, Roberta Marziani, Caterina Ida Zeppieri
2022-05-30
Computational Engineering, Finance, and Science · Computer Science
Second-order phase-field formulations for anisotropic brittle fracture
Tymofiy Gerasimov, Laura De Lorenzis
2021-12-22
Analysis of PDEs · Mathematics
Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation
Maicol Caponi
2025-10-06
Analysis of PDEs · Mathematics
Homogenisation of phase-field functionals with linear growth
Francesco Colasanto, Matteo Focardi, Caterina Ida Zeppieri
2026-05-12
Analysis of PDEs · Mathematics
Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study
Veronika Auer-Volkmann, Lisa Beck, Bernd Schmidt
2022-02-01
Computational Engineering, Finance, and Science · Computer Science
Phase-field modeling of fracture for quasi-brittle materials
Jacinto Ulloa, Patricio Rodríguez, Cristóbal Samaniego, Esteban Samaniego
2019-03-01
Analysis of PDEs · Mathematics
Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation
Sandro Belz, Kristian Bredies
2021-09-27
Applied Physics · Physics
A variational approach to fracture incorporating any convex strength criterion
Blaise Bourdin, Jean-Jacques Marigo, Corrado Maurini, Camilla Zolesi
2025-07-01
Analysis of PDEs · Mathematics
Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy
Sergio Conti, Matteo Focardi, Flaviana Iurlano
2022-05-16
Analysis of PDEs · Mathematics
Functionals defined on piecewise rigid functions: Integral representation and $\Gamma$-convergence
Manuel Friedrich, Francesco Solombrino
2020-02-04
Numerical Analysis · Mathematics
Discrete approximation of the Griffith functional by adaptive finite elements
Jean-François Babadjian, Élise Bonhomme
2023-06-16
Analysis of PDEs · Mathematics
Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions
Antonio Flavio Donnarumma, Manuel Friedrich
2023-12-20