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 …
obtained by alternate minimization schemes. First, we characterize their time-continuous …
Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue
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 …
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 …
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 …
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
We study the approximation of finite-dimensional rate-independent quasistatic systems, via
a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform …
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
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 …
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
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 …
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
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 …
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 …
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
We consider generalized gradient systems in Banach spaces whose evolutions are
generated by the interplay between an energy functional and a dissipation potential. We …
generated by the interplay between an energy functional and a dissipation potential. We …