Nonlocal strain-softening model of quasi-brittle materials using boundary element method

Lin, Feng; Geng, Yanfen; Bažant, Zdeněk P.; Ding, Fangming

doi:10.1016/s0955-7997(01)00110-2

Cited by 21 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient elastoplastic analysis with the boundary element method

2007

View full text Add to dashboard Cite

show abstract

“…This integral-type non-local formulation for material softening, which is usually more e ective than the weakly non-local formulation for treating problems with softening damage, for example distributed cracking, has apparently not yet been presented in the literature (except for the preceding study [36]) and is taken as the objective of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…In a parallel study [36], in which a simpler, but theoretically less appealing, version of the boundary element method is generalized for non-local behaviour, other numerical examples are analysed to conÿrm that the concept of a non-local plasticity model exhibits correct and rapid convergence at mesh reÿnements and avoids spurious mesh sensitivity. In that study, for the sake of simplicity, only the standard non-regularized integral representations are used.…”

Section: Introductionmentioning

confidence: 99%

Non‐local boundary integral formulation for softening damage

Sládek

Bažant

2003

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYA strongly non-local boundary element method (BEM) for structures with strain-softening damage treated by an integral-type operator is developed. A plasticity model with yield limit degradation is implemented in a boundary element program using the initial-stress boundary element method with iterations in each load increment. Regularized integral representations and boundary integral equations are used to avoid the di culties associated with numerical computation of singular integrals. A numerical example is solved to verify the physical correctness and e ciency of the proposed formulation. The example consists of a softening strip perforated by a circular hole, subjected to tension. The strainsoftening damage is described by a plasticity model with a negative hardening parameter. The local formulation is shown to exhibit spurious sensitivity to cell mesh reÿnements, localization of softening damage into a band of single-cell width, and excessive dependence of energy dissipation on the cell size. By contrast, the results for the non-local theory are shown to be free of these physically incorrect features. Compared to the classical non-local ÿnite element approach, an additional advantage is that the internal cells need to be introduced only within the small zone (or band) in which the strain-softening damage tends to localize within the structure.

show abstract

“…The arclength constraint, added to the governing integral equations, forms a nonlinear system of equations which is solved by applying directly the Newton-Raphson method. Only in 2002-2003 have Lin et al (2002) and Sládek et al (2003) incorporated an integral type nonlocal strain softening localisation limiter into the BDEM; nevertheless, they use a formulation which both gives some locking effects in FE and they cannot deal with snap-back behaviours. In Alessandri et al (2000) a nonlocal integral formulation for elastic-damaging materials is presented.…”

mentioning

confidence: 99%

Integral equations and nonlocal damage theory: a numerical implementation using the BDEM

Mallardo

2008

Int J Fract

View full text Add to dashboard Cite

In this paper the integral equation approach is developed to describe elastic-damaging materials. An isotropic damage model is implemented to study nonlinear structural problems involving localisation phenomena. Especially for the cases that exhibit stress or strain concentrations, an integral approach can be recommended. Besides, the technique is able to represent well high gradients of stress/strain. The governing integral equations are discretised by using quadratic isoparametric elements on the boundary and quadratic continuous/discontinuous cells in the zone where the nonlinear phenomenon occurs. Two numerical examples are presented to show the physical correctness and efficiency of the proposed procedure. The results are compared with the local theory and they turn out to be free of the spurious sensitivity to cell mesh refinement

show abstract

Nonlocal strain-softening model of quasi-brittle materials using boundary element method

Cited by 21 publications

References 13 publications

Efficient elastoplastic analysis with the boundary element method

Efficient elastoplastic analysis with the boundary element method

Non‐local boundary integral formulation for softening damage

Integral equations and nonlocal damage theory: a numerical implementation using the BDEM

Contact Info

Product

Resources

About