A finite deformation continuum\discrete model for the description of fragmentation and damage in brittle materials (original) (raw)
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Discrete Element Model for Brittle Fracture
We adopt the discrete element method (DEM) to study the fracture behavior of brittle materials. We propose an approach which relates crack initiation to crack growth. The material consists of a set of particles in contact, which allows us to derive an expression for the stress intensity factor as a function of the contact forces and displacements. A classical failure criterion, based on the material’s toughness, is then adopted for the analysis of crack propagation, represented by the loss of cohesion forces between particles. Afterwards, we apply our discrete criterion to uncracked materials under homogenous stress conditions, obtaining a Rankine like behavior. The work results in a simple discrete model which is totally compatible to continuum mechanics, where no calibration tests are required, in contrast to most of discrete approaches
A Discrete Element Approach in Fracture Mechanics of Brittle Materials
2011
In this study, we use the discrete element method (DEM) to model the fracture behavior of brittle materials in 2D. The material consists of a set of particles in contact with a close-packed structure. It allows us to derive an expression for the stress intensity factor as a function of the contact forces near the crack tip. A classical failure criterion, based on the material's toughness, is then adopted in the analysis of mixed mode crack propagation, represented by the contact loss between particles. We compare our model to classical solutions of tensile crack (mode I) and shear crack (mode II). 1 INTRODUCTION The discrete element method (DEM) [1] is generally used in contact problems of a large number of particles. Material properties like elasticity, plasticity, viscosity, etc. can be modeled with different contact laws between particles. The introduction of bonded contacts with a limited resistance allow us to model brittle materials in fracture problems [2]. Although realistic macroscopic brittle behaviors are obtained with these models, a previous calibration of the contact laws is required [3]. Recent work of [4] presents analytical expressions which relate directly DEM material parameters to elastic continuous solid parameters (i.e. Young's modulus and Poisson's ratio). These expressions are based on a bidimensional close-packed assembly of particles. Considering this equivalence between discrete and continuous models in elasticity, we propose a DEM approach in fracture mechanics for brittle materials. The concordance with continuous classical theories exempt us of any previous calibration of the model parameters in order to attain convergent results. This article begins with a presentation of the elastic contact law adopted in our simulations in Sec. 2. In Sec. 3, we present the theoretical elements of our discrete model in fracture mechanics. We compare our numerical results to classical cases of tensile and shear fracture in Sec. 4. Finally we present the conclusions of the work.
A discrete model for fracture of rigid solids based on a damaging interface
We describe the progressive and delayed fracture of rigid solids by a discrete modelling. Each rigid solid is considered as an assembly of particles with initial cohesive bonds, the latter decreasing progressively during the loading. A damaging interface model is proposed to describe this progressive phenomenon. This model has been implemented in a numerical code based on a discrete element method. The illustrative example is related to the crushing of an assembly of rigid solids -i.e. a granular medium -due to an oedometric compression.
Fracture of rigid solids: a discrete approach based on damaging interface modelling
Comptes Rendus Mecanique, 2007
We describe the progressive and delayed fracture of rigid solids by a discrete modelling. Each rigid solid is considered as an assembly of particles with initial cohesive bonds, the latter decreasing progressively during the loading. A damaging interface model is proposed to describe this progressive phenomenon. The model has been implemented in a discrete element code. The first illustrative example, which is actually a parametric study, deals with the progressive damage and sudden fracture of a single interface submitted to an uniaxial tension. The second example is related to the crushing of an assembly of rigid solids-i.e. a granular medium-submitted to an oedometric compression. To cite this article: C. Silvani et al., C. R. Mecanique 335 (2007).
Dynamic damage and fracture processes in brittle materials
Dynamic Behavior of Materials, 2024
Brittle materials such as, rocks, concrete and high-performance concrete, glass, ceramics, ice..., are materials abundantly present in our everyday life and materials involved in many industrial applications or in various protective solutions. Achieving a good understanding of their strain-rate sensitivity in relation with their microstructure remains a major issue. In addition, the development of micromechanics-based models is of major importance in view of improving the predictive capabilities of analytical and numerical models and in order to better explain the role of material parameters involved in the strain-rate and pressure sensitivity of brittle materials. In the present chapter the damage and fracture processes involved in various brittle materials are discussed. Several experimental techniques offering the capability to characterize and analyse these damage modes are presented. Next, some micromechanics-based models attending to describe these mechanisms are detailed. Experimental and modelling approaches allow highlighting the main microstructural parameters driving the behaviour of brittle materials at high loading rates.
A new continuum model to describe damage, fragmentation and large deformation of pulverized brittle materials is presented. The multiple-plane-microcracking (MPM) model, developed by Espinosa, has been modiÿed to track microcracking on 13 orientations under high pressure, high strain rate and high deformation. This model provides the elastic and inelastic response of the material before massive crack coalescence. When pulverization occurs, the constitutive response is modelled by means of a viscoplastic model for granular material, which is a generalization to three dimensions of the double-sliding theory augmented by a consolidation mechanism. The initialization of the granular model is governed by a yield surface at the onset of massive crack coalescence. This is accomplished by examining a representative volume element, modelled using the MPM model, in compression-shear. The main advantage of this approach is to keep a continuum model at all stages of the deformation process and thus avoid the di culties of crack representation in a discrete ÿnite element code. This model has been implemented in LS-DYNA and used to examine interface defeat of long rod penetrators by a conÿned ceramic plate. The numerical simulations are compared to experiments in order to identify failure modes. The model parameters were obtained independently by simulating plate and rod impact experiments. The proposed model captures most of the physical observations as well as failure mode transition, from interface defeat to full penetration, with increasing impact velocity.
International Journal for Numerical Methods in Engineering, 2002
A new continuum model to describe damage, fragmentation and large deformation of pulverized brittle materials is presented. The multiple-plane-microcracking (MPM) model, developed by Espinosa, has been modiÿed to track microcracking on 13 orientations under high pressure, high strain rate and high deformation. This model provides the elastic and inelastic response of the material before massive crack coalescence. When pulverization occurs, the constitutive response is modelled by means of a viscoplastic model for granular material, which is a generalization to three dimensions of the double-sliding theory augmented by a consolidation mechanism. The initialization of the granular model is governed by a yield surface at the onset of massive crack coalescence. This is accomplished by examining a representative volume element, modelled using the MPM model, in compression-shear. The main advantage of this approach is to keep a continuum model at all stages of the deformation process and thus avoid the di culties of crack representation in a discrete ÿnite element code. This model has been implemented in LS-DYNA and used to examine interface defeat of long rod penetrators by a conÿned ceramic plate. The numerical simulations are compared to experiments in order to identify failure modes. The model parameters were obtained independently by simulating plate and rod impact experiments. The proposed model captures most of the physical observations as well as failure mode transition, from interface defeat to full penetration, with increasing impact velocity.
Discrete element approach in brittle fracture mechanics
Engineering Computations, 2013
Purpose-The purpose of this paper is to use the discrete element method (DEM) to model the fracture behaviour of brittle materials in 2D. Design/methodology/approach-The material consists of a set of particles in contact with a close-packed structure. It allows the derivation of an expression for the stress intensity factor as a function of the contact forces near the crack tip. A classical failure criterion, based on the material's toughness, is then adopted for the analysis of crack propagation, represented by the contact loss between particles. Findings-The DEM approach is compared to two tensile cases (mode I); both presenting a monotonous convergence towards classical solutions for more precise discretization. Originality/value-The paper proposes a DEM approach in fracture mechanics of isotropic brittle materials entirely compatible with continuous classical theory. Hence the toughness value is directly introduced as a parameter of the material without any previous calibration of the DEM.
Damage evolution during microcracking of brittle solids
Acta Materialia, 2001
Microcracking due to thermal expansion and elastic anisotropy is examined via computer simulations with a microstructural-based finite element model. Random polycrystalline microstructures are generated via Monte Carlo Potts-model simulations. Microcrack formation and propagation due to thermal expansion anisotropy is investigated in these microstructures using a Griffith-type failure criterion in a microstructuralbased finite element model called OOF. Effects of the grain size distribution on the accumulation of microcrack damage, as well as on the threshold for microcrack initiation, are analysed. Damage evolution is rationalised by statistical considerations, i.e. damage accumulation is correlated with the statistical distributions of microstructural parameters.