Fatigue effects in elastic materials with variational damage models: A vanishing viscosity approach
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 …
which take into account fatigue, that is the process of weakening in a material due to …
Balanced viscosity solutions to a rate-independent system for damage
D Knees, R Rossi, C Zanini - European Journal of Applied …, 2019 - cambridge.org
This article is the third one in a series of papers by the authors on vanishing-viscosity
solutions to rate-independent damage systems. While in the first two papers (Knees, D. et al …
solutions to rate-independent damage systems. While in the first two papers (Knees, D. et al …
Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics
We study the convergence of an alternate minimization scheme for a Ginzburg–Landau
phase-field model of fracture. This algorithm is characterized by the lack of irreversibility …
phase-field model of fracture. This algorithm is characterized by the lack of irreversibility …
Analysis of staggered evolutions for nonlinear energies in phase field fracture
We consider a class of separately convex phase field energies employed in fracture
mechanics, featuring non-interpenetration and a general softening behavior. We analyze the …
mechanics, featuring non-interpenetration and a general softening behavior. We analyze the …
A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity
In this paper, we derive a new 2D brittle fracture model for thin shells via dimension
reduction, where the admissible displacements are only normal to the shell surface. The …
reduction, where the admissible displacements are only normal to the shell surface. The …
Balanced viscosity solutions to a rate-independent coupled elasto-plastic damage system
A rate-independent model coupling small-strain associative elasto-plasticity and damage is
studied via a vanishing-viscosity analysis with respect to all the variables describing the …
studied via a vanishing-viscosity analysis with respect to all the variables describing the …
Phase‐Field Fracture at Finite Strains Based on Modified Invariants: A Note on its Analysis and Simulations
M Thomas, C Bilgen, K Weinberg - GAMM‐Mitteilungen, 2018 - Wiley Online Library
We present recent results on the mathematical analysis of phase‐field model for anisotropic
fracture at finite strains. It is based on a modification of the Ambrosio‐Tortorelli model …
fracture at finite strains. It is based on a modification of the Ambrosio‐Tortorelli model …
Existence of solutions to a phase–field model of dynamic fracture with a crack–dependent dissipation
M Caponi - Nonlinear Differential Equations and Applications …, 2020 - Springer
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 …
approximation, which takes into account dissipative effects due to the speed of the crack tips …
On some mathematical problems in fracture dynamics
M Caponi - 2019 - iris.sissa.it
This thesis is devoted to the study of several mathematical problems in fracture mechanics
for brittle materials. In the first part, we prove existence, uniqueness, and continuous …
for brittle materials. In the first part, we prove existence, uniqueness, and continuous …
Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity
R Rossi - Mathematical Models and Methods in Applied …, 2019 - World Scientific
This paper revolves around a newly introduced weak solvability concept for rate-
independent systems, alternative to the notions of Energetic (E) and Balanced Viscosity (BV) …
independent systems, alternative to the notions of Energetic (E) and Balanced Viscosity (BV) …