Related papers: Variational problems in fracture mechanics

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids \emph{not} just under monotonic but under general loading conditions, this paper puts forth…

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…

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…

This work presents a critical overview of the effects of different aspects of model formulation on crack path selection in quasi-static phase field fracture. We consider different evolution methods, mechanics formulations, fracture…

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We…

This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…

We examine theoretically and numerically fast propagation of a tensile crack along unidimensional strips with periodically evolving toughness. In such dynamic fracture regimes, crack front waves form and transport front disturbances along…

Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is…

We present a numerical implementation of a model of quasi-static crack growth in linearly elastic-perfectly plastic materials. We assume that the displacement is antiplane, and that the cracks and the plastic slips are localized on a…

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…

We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local,…

Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…

Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of…

In this paper, we augment existing techniques for simulating flexible objects to include models for crack initiation and propagation in three-dimensional volumes. By analyzing the stress tensors computed over a finite element model, the…

In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…

Despite advances in manufacturing making metal functionally graded materials (FGMs) more common, numerical methods for predicting fracture in ductile functionally graded materials remain limited. In this work we study the crack propagation…

We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…

Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation…

We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco-elastic/plastic parts. The constitutive…