Related papers: Adaptive finite element approximation for quasi-st…
We propose a model for quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and…
Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the spirit of this novel concept,…
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model…
In this work, the finite elements method (FEM) is used to analyse the growth of fretting cracks. FEM can be favourably used to extract the stress intensity factors in mixed mode, a typical situation for cracks growing in the vicinity of a…
We present a finite-size study of the athermal quasistatic yielding transition in structural glasses featuring a wide range of mechanical disorder. We find a crossover from gradual yielding in small systems, to a macroscopic discontinuous…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
We formulate a nonlocal cohesive model for calculating the deformation state inside a cracking body. In this model a more complete set of physical properties including elastic and softening behavior are assigned to each point in the medium.…
We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using…
A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…
This paper addresses the question of the interplay between relaxation and irreversibility through quasi-static evolutions in damage mechanics, by inquiring the following question: can the quasi-static evolution of an elastic material…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evolution, as the size of the layers vanishes. The limit…
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…
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 consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…
We examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a regularized finite-time singularity, with…