Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples

Loret, Benjamin; Prévost, Jean‐Hérve

doi:10.1016/0045-7825(90)90073-u

Cited by 191 publications

(69 citation statements)

References 28 publications

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“…Rate-dependent plasticity models contain an intrinsic length scale that regularizes the mesh pathology associated with the rate-independent limit, while generating a well-posed governing PDE (Sandler and Wright, 1984;Needleman, 1988;Loret and Prevost, 1990). Here, though it is of interest to consider the rate-independent case directly since many geomechanical initial boundary value problems entail loading rates slow enough such that the rate-independent limit is appropriate.…”

Section: Introductionmentioning

confidence: 99%

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Regueiro

Borja

2001

International Journal of Solids and Structures

113

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Numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization. Many regularization techniques have been proposed to address the ill posedness associated with rate-independent softening plasticity that leads to mesh-dependent numerical simulations. One approach to alleviating mesh dependence is the strong discontinuity approach, which represents localized deformation as a slip surface within a plasticity model; a strong discontinuity is a discontinuous displacement ®eld. This approach is used in this paper to formulate a plane strain, pressure sensitive, nonassociative plasticity model with strong discontinuity and to implement the model, along with an enhanced bilinear quadrilateral element, via an assumed enhanced strain method. Numerical examples demonstrate mesh independence of the method for pressure sensitive materials. Ó

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Section: Introductionmentioning

confidence: 99%

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Regueiro

Borja

2001

International Journal of Solids and Structures

113

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“…For more details, the reader is referred to numerous articles and books on damage mechanics [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The use of strain-softening material models leads to an ill-posed boundary value problem (BVP) [27][28][29][30][31]. The solution of ill-posed BVPs with computational methods leads to certain difficulties.…”

Section: Introductionmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

161

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…The standard finite element solution of strain localization in a rate-dependent material results in solutions that is strongly mesh-sensitive. Higher order constitutive models can solve this problem: viscoplastic model 12) , non local theory 13) , gradient elasto-plastic model 14) , otherwise, Gudehus & Nubel 15) , showed the size of elements has to be in the order of 3D 50 . Such fine mesh size prohibits the rigorous application of FE method to real-scaled problems.…”

Section: Numerical Modelingmentioning

confidence: 99%

Experimental Validation of a Numerical Model: Reverse Fault Rupture Propagation Through Sand

Rokonuzzaman

Sakai

Nahas

et al. 2009

JSCE JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING

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In this study, a sophisticated numerical model incorporating a hardening-softening constitutive model with shear band is calibrated from the direct shear test results, and validated for the prediction of the behaviour of medium dense Fotainebleau sand bed for quasi-static displacement induced by reverse fault's base rock with dip angle of 60°. The vertical displacements profile of the ground surface, minimum vertical base displacement for the rupture to reach the ground, the average dip angle propagated into the soil as well as the horizontal extent of the deformed surface ground due to different stress fields (centrifuge and 1g tests) are evaluated by having close agreement between experiments and numerical analyses.

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Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples

Cited by 191 publications

References 28 publications

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Experimental Validation of a Numerical Model: Reverse Fault Rupture Propagation Through Sand

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