Fatigue effects in elastic materials with variational damage models: A vanishing viscosity approach

R Alessi, V Crismale, G Orlando - Journal of Nonlinear Science, 2019 - Springer
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 …

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 …

Convergence of discrete and continuous unilateral flows for Ambrosio–Tortorelli energies and application to mechanics

S Almi, S Belz, M Negri - ESAIM: Mathematical Modelling and …, 2019 - esaim-m2an.org
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 …

Analysis of staggered evolutions for nonlinear energies in phase field fracture

S Almi, M Negri - Archive for Rational Mechanics and Analysis, 2020 - Springer
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 …

A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity

S Almi, S Belz, S Micheletti, S Perotto - Mathematical Models and …, 2021 - World Scientific
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 …

Balanced viscosity solutions to a rate-independent coupled elasto-plastic damage system

V Crismale, R Rossi - SIAM Journal on Mathematical Analysis, 2021 - SIAM
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 …

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 …

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 …

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 …

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) …