相关论文: Consistent Finite-Dimensional Approximation of Pha…

We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…

We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions…

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…

We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the…

We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of a brittle fracture proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the…

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite…

The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the…

The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the…

We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…

This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…

We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffith's criterion. We restrict our…

Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include complex evolution of…

We propose and analyze an adaptive finite element method for a phase-field model of dynamic brittle fracture. The model couples a second-order hyperbolic equation for elastodynamics with the Ambrosio-Tortorelli regularization of the…

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of…

The main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying…

In this paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with…

We study the atomistic-to-continuum limit for a model of a quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spring system whose interactions are modeled by classical…