Computational modelling of impact damage in brittle materials

Camacho, Guamán; Ortiz, Michael

doi:10.1016/0020-7683(95)00255-3

Cited by 1,807 publications

(1,071 citation statements)

References 44 publications

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“…More recently, these methods have evolved into approaches for which cohesive surfaces are introduced adaptively along element interfaces. Ortiz et al have used an adaptive approach for a variety of simulations of dynamic fracture and fragmentation in both two [15,16] and three [70,81] dimensions. Use of a network cohesive surfaces for simulating generalized fracture within a finite element setting was pioneered by Xu and Needleman [95,96].…”

Section: Introductionmentioning

confidence: 99%

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

151

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Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.

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Section: Introductionmentioning

confidence: 99%

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

151

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“…If the equivalent traction at any of the Gauss points in the element ahead of the crack tip exceeds the cohesive strength, the crack is extended into that element until it touches one of the element edges. The equivalent traction t eq is computed from the tractions of an averaged effective stress tensor at the crack tip [21]:…”

Section: Finite Element Implementationmentioning

confidence: 99%

A large deformation formulation for fluid flow in a progressively fracturing porous material

Irzal

Remmers

Huyghe

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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ReuseThis article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can't change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.A large deformation formulation for fluid flow in a progressively fracturing porous material AbstractA general numerical model has been developed for fluid flow in a progressively fracturing porous medium subject to large deformations. The fluid flow away from the crack is modelled in a standard manner using Darcy's relation, while in the discontinuity Stokes' flow is assumed, taking into account the change of permeability due to progressive damage evolution inside the crack. The crack is described in a discrete manner by exploiting the partition-of-unity property of finite element shape functions. The nucleation and the opening of micro-cracks are modelled by a tractionseparation relation. A heuristic approach is adopted to model the orientation of the cracks at the interfaces in the deformed configuration. A two-field formulation is derived, with the solid and the fluid velocities as unknowns. The weak formulation is derived next, assuming a Total Lagrangian formulation. This naturally leads to a set of coupled equations for the continuous and for the discontinuous parts of the mixture. The resulting discrete equations are nonlinear due to the cohesive-crack model, the large-deformation kinematic relations, and the coupling terms between the fine scale and the coarse scale. The capabilities of the model are shown at the hand of some example problems.

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“…When a potential for the cohesive crack is defined, the unidirectional stress-displacement relation can be extended to general mixed mode problems, as in [36,37,38]. Note that if only one-dimensional cohesive models for mode-I fracture are employed, traction continuity is in general violated.…”

Section: Cohesive Cracksmentioning

confidence: 99%

Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment

Bordas

Zi²,

Rabczuk

2007

IUTAM Symposium on Discretization Methods for Evolving Discontinuities

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This paper presents a three-dimensional, extrinsically enriched meshfree method for initiation, branching, growth and coalescence of an arbitrary number of cracks in non-linear solids including large deformations, for statics and dynamics. The novelty of the methodology is that only an extrinsic discontinuous enrichment and no near-tip enrichment is required. Instead, a Lagrange multiplier field is added along the crack front to close the crack. This decreases the computational cost and removes difficulties involved with a branch enrichment. The results are compared to experimental data, and other simulations from the literature to show the robustness and accuracy of the method.

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Computational modelling of impact damage in brittle materials

Cited by 1,807 publications

References 44 publications

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

A large deformation formulation for fluid flow in a progressively fracturing porous material

Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment

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