相关论文: Linearization of quasistatic fracture evolution in…

In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed…

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…

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…

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…

Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture…

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 show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of…

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\ge1$, with a quasiconvex bulk…

This paper deals with the quasistatic crack growth of a homogeneous elastic brittle thin film. It is shown that the quasistatic evolution of a three-dimensional cylinder converges, as its thickness tends to zero, to a two-dimensional…

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

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…

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 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…

The paper is devoted to the study of quasi-static brittle crack evolution. We work under the following assumptions: a linear elastic body, with or without initial cracks inside, evolves in a quasi-static manner under an imposed path of…

We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed in [13] by G. Dal Maso, G.A. Francfort, and R. Toader, which takes into account body forces and surface loads.…

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…

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 that the density of the energy dissipated in the…

In this paper we contribute to studying the issue of quasistatic limit in the context of Griffith's theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate…

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…