Convergence of alternate minimization schemes for phase-field fracture and damage

D Knees, M Negri - Mathematical Models and Methods in Applied …, 2017 - World Scientific
We consider time-discrete evolutions for a phase-field model (for fracture and damage)
obtained by alternate minimization schemes. First, we characterize their time-continuous …

Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue

V Crismale, G Lazzaroni, G Orlando - Mathematical Models and …, 2018 - World Scientific
In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a
prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is …

Convergence of critical points for a phase-field approximation of 1d cohesive fracture energies

M Bonacini, F Iurlano - Calculus of Variations and Partial Differential …, 2024 - Springer
Variational models for cohesive fracture are based on the idea that the fracture energy is
released gradually as the crack opening grows. Recently, proposed a variational …

Convergence analysis of time-discretisation schemes for rate-independent systems

D Knees - ESAIM: Control, Optimisation and Calculus of …, 2019 - esaim-cocv.org
It is well known that rate-independent systems involving nonconvex energy functionals in
general do not allow for time-continuous solutions even if the given data are smooth. In the …

A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers

P Gidoni, F Riva - Calculus of Variations and Partial Differential …, 2021 - Springer
We study the approximation of finite-dimensional rate-independent quasistatic systems, via
a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform …

On the quasistatic limit of dynamic evolutions for a peeling test in dimension one

G Lazzaroni, L Nardini - Journal of Nonlinear Science, 2018 - Springer
The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic
debonding. We start from a dynamic problem that strongly couples the wave equation in a …

Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy

S Conti, M Focardi, F Iurlano - Archive for Rational Mechanics and …, 2024 - Springer
We consider a family of vectorial models for cohesive fracture, which may incorporate SO (n)-
invariance. The deformation belongs to the space of generalized functions of bounded …

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 …

Viscous corrections of the time incremental minimization scheme and visco-energetic solutions to rate-independent evolution problems

L Minotti, G Savaré - Archive for Rational Mechanics and Analysis, 2018 - Springer
We propose the new notion of Visco-Energetic solutions to rate-independent systems (X,
E,(X, E, d) driven by a time dependent energy EE and a dissipation quasi-distance d in a …

On time-splitting methods for gradient flows with two dissipation mechanisms

A Mielke, R Rossi, A Stephan - Calculus of Variations and Partial …, 2025 - Springer
We consider generalized gradient systems in Banach spaces whose evolutions are
generated by the interplay between an energy functional and a dissipation potential. We …