Non‐local boundary integral formulation for softening damage

Sládek, J.; Sládek, V.; Bažant, Zdeněk P.

doi:10.1002/nme.673

Cited by 29 publications

(8 citation statements)

References 27 publications

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“…Due to the dimension-reduction, the remeshing procedure is fairly simple as the crack is part of the boundary. Interesting applications of the BEM to fracture can be found, for example, in [240][241][242][243][244][245][246][247][248][249][250][251][252][253][254][255][256][257].…”

Section: Boundary Element Methodmentioning

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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Section: Boundary Element Methodmentioning

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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“…Examples include sensitivity analyses [5], dynamical loadings [6,7], shear band formation [8], gradient plasticity [9,10], thermo-elasto-plasticity [11], and large strains [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A new boundary element technique without domain integrals for elastoplastic solids

Bertoldi

Brun

Bigoni

2005

Numerical Meth Engineering

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A simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements, namely, to use the Green's functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions, respectively. In this way, domain integrals are completely avoided in the boundary integral equations. Though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation, the elastoplastic analysis reduces, in essence, to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations (the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law). Numerical examples, using J(2)-flow theory with linear hardening, demonstrate that the proposed method retains all the advantages related to boundary element formulations, is stable and performs well.\ud \ud The method presented is for simplicity developed for the associative flow rule; however, a full derivation of Green's function and boundary integral equations is also given for the general case of non-associative flow rule. It is shown that in the non-associative case, a domain integral unavoidably arises in the formulation

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“…The approach used to compute the domain integrals is to adopt internal cells, see for example [2,9,14,16,17,21,[26][27][28][29][30]33,[35][36][37][38][39][40][41][43][44][45][46]50,[53][54][55][56][57][59][60][61]63,65,66]. These cells are like finite elements in appearance, but the main difference is that they do not introduce any additional unknowns to the problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient elastoplastic analysis with the boundary element method

2007

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Conventional numerical implementation of the boundary element method (BEM) for elasto-plastic analysis requires a domain discretization into cells. This requires more effort for the discretization of the problem and additional computational effort. A new technique is proposed here for the analysis of 2D and 3D elasto-plastic problems with the boundary element method. In this approach the domain does not need to be discretised into cells prior to the analysis. Plasticity is assumed to start from the boundary and the cells are generated from the boundary data automatically during the analysis. Using the cell generation process, elasto-plastic analysis with the BEM becomes much more user friendly and efficient than the standard approach with a pre-definition of cells. The accuracy and efficiency of the solution obtained by the new approach is verified by several numerical examples.

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Non‐local boundary integral formulation for softening damage

Cited by 29 publications

References 27 publications

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

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

A new boundary element technique without domain integrals for elastoplastic solids

Efficient elastoplastic analysis with the boundary element method

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