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A fast boundary element based solver for localized inelastic deformations
Author(s) -
Ciardo Federico,
Lecampion Brice,
Fayard François,
Chaillat Stéphanie
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6520
Subject(s) - solver , discretization , preconditioner , boundary element method , discontinuity (linguistics) , classification of discontinuities , finite element method , nonlinear system , mathematics , mathematical analysis , geometry , structural engineering , physics , linear system , mathematical optimization , engineering , quantum mechanics
Summary We present a numerical method for the solution of nonlinear geomechanical problems involving localized deformation along shear bands and fractures. We leverage the boundary element method to solve for the quasi‐static elastic deformation of the medium while rigid‐plastic constitutive relations govern the behavior of displacement discontinuity (DD) segments capturing localized deformations. A fully implicit scheme is developed using a hierarchical approximation of the boundary element matrix. Combined with an adequate block preconditioner, this allows to tackle large problems via the use of an iterative solver for the solution of the tangent system. Several two‐dimensional examples of the initiation and growth of shear‐bands and tensile fractures illustrate the capabilities and accuracy of this technique. The method does not exhibit any mesh dependency associated with localization provided that (i) the softening length‐scale is resolved and (ii) the plane of localized deformations is discretized a priori using DD segments.