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A bonded-particle model for rock

Meshless methods: An overview and recent developments

A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

Cracking particles: A simplified meshfree method for arbitrary evolving cracks

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

The extended/generalized finite element method: An overview of the method and its applications

Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. A great variety of nonlocal models have appeared during the last two decades. This paper reviews the progress in the nonlocal models of integral type, and discusses their physical justifications, advantages, and numerical applications.

Nonlocal integral formulations of plasticity and damage: Survey of progress

A particle model for brittle aggregate composite materials such as concretes, rocks, or ceramics is presented. The model is also applicable to the behavior of unidirectionally reinforced fiber composites in the transverse plane. A method of random computer generation of the particle system meeting the prescribed particle size distribution is developed. The particles are assumed to be elastic and have only axial interactions, as in a truss. The interparticle contact layers of the matrix are described by a softening stress‐strain relation corresponding to a prescribed microscopic interparticle fracture energy. Both two‐ and three‐dimensional versions of the model are easy to program, but the latter poses, at present, forbidding demands for computer time. The model is shown to simulate realistically the spread of cracking and its localization. Furthermore, the model exhibits a size effect on: (1) The nominal strength, agreeing with the previously proposed size effect law; and (2) the slope of the post‐peak l...

Random particle model for fracture of aggregate or fiber composites

Element-free galerkin methods for static and dynamic fracture

The element-free Galerkin method for dynamic crack propagation is described and applied to several problems. This method is a gridless method, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces. The essential feature of the method is the use of moving least-squares interpolants for the trial-and-test functions. In these interpolants, the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point. The discrete equations are obtained by a Galerkin method. The procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described.

Dynamic fracture using element-free galerkin methods

Element-free Galerkin method for wave propagation and dynamic fracture

Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L 2 -projection of strains is the most effective for the constant strain elements considered here. Examples of one-dimensional and two-dimensional localization (shear band formation) problems are given

Mazen R. Tabbara

Papers

Random particle model for fracture of aggregate or fiber composites

Element-free galerkin methods for static and dynamic fracture

Dynamic fracture using element-free galerkin methods

Element-free Galerkin method for wave propagation and dynamic fracture

H-adaptive finite element methods for dynamic problems, with emphasis on localization