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Related papers: Gradient damage models for heterogeneous materials

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We study the $\Gamma$-convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction of…

Analysis of PDEs · Mathematics 2018-03-09 Marco Caroccia , Nicolas Van Goethem

We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…

Analysis of PDEs · Mathematics 2021-11-17 Mark A. Peletier , Mikola C. Schlottke

The precise mechanisms underlying the failure of multi-phase materials may be strongly dependent on the material's microstructural morphology. Micromechanical modeling has provided much insight into this dependence, but uncertainties remain…

Materials Science · Physics 2016-04-14 T. W. J. de Geus , R. H. J. Peerlings , M. G. D. Geers

We propose a phase-field model of dynamic fracture based on the Ambrosio--Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in…

Analysis of PDEs · Mathematics 2025-10-06 Maicol Caponi

In this paper we first give a brief overview of Monte Carlo simulation results obtained by applying the Damage Spreading method. We analyse the transition between a state where the damage becomes healed (the frozen phase) and a regime where…

Statistical Mechanics · Physics 2008-03-12 M. Leticia Rubio Puzzo , Ezequiel V. Albano

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…

Materials Science · Physics 2018-03-14 Juan Michael Sargado , Eirik Keilegavlen , Inga Berre , Jan Martin Nordbotten

A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…

Applied Physics · Physics 2018-04-04 Armand Wirgin

We obtain a cohesive fracture model as a $\Gamma$-limit of scalar damage models in which the elastic coefficient is computed from the damage variable $v$ through a function $f_k$ of the form $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, with…

Analysis of PDEs · Mathematics 2018-05-01 Sergio Conti , Matteo Focardi , Flaviana Iurlano

We analyze the $\Gamma$-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove…

Analysis of PDEs · Mathematics 2020-10-15 Manuel Friedrich , Matteo Perugini , Francesco Solombrino

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with…

We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…

Optimization and Control · Mathematics 2024-05-01 Patrick Dondl , Alberto Maione , Steve Wolff-Vorbeck

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…

Computational Engineering, Finance, and Science · Computer Science 2019-03-01 Jacinto Ulloa , Patricio Rodríguez , Cristóbal Samaniego , Esteban Samaniego

We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while…

We analyze a finite-difference approximation of a functional of Ambrosio-Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $\delta$…

Analysis of PDEs · Mathematics 2020-07-31 Vito Crismale , Giovanni Scilla , Francesco Solombrino

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…

Materials Science · Physics 2011-07-28 Daniel A. Cogswell , W. Craig Carter

We investigate the $\Gamma$-convergence of Ambrosio-Tortorelli type-functionals for circle valued functions, in the case of volume terms with linear growth. We show the emergence of a non-local $\Gamma$-limit, which is due to the…

Analysis of PDEs · Mathematics 2026-01-29 Giovanni Bellettini , Roberta Marziani , Riccardo Scala

In recent years, various phase field models have been developed in variational methods to simulate the failure of brittle solids. However, there is a lack of objective evaluation of the existing results, and in particular, there are few…

Numerical Analysis · Mathematics 2021-09-23 Yuanfeng Yu , Xiaoya Zheng , Peng Li , Zhongzhou Zhang , Jinyou Xiao

A novel phase-field for ductile fracture model is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling…

Materials Science · Physics 2021-03-24 Tianchen Hu , Brandon Talamini , Andrew J. Stershic , Michael R. Tupek , John E. Dolbow

In this paper we studythe asymptotics of singularly perturbed phase-transition functionals of the form \[ F_k(u)=\frac{1}{\epsilon_k}\int_A f_k(x,u,\epsilon_k\nabla u)\,dx\,, \] where $u \in [0,1]$ is a phase-field variable, $\epsilon_k>0$…

Analysis of PDEs · Mathematics 2022-06-29 Roberta Marziani

We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the…

Analysis of PDEs · Mathematics 2020-09-24 Roberto Alessi , Vito Crismale , Gianluca Orlando