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.

中文翻译：

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一种基于边界元的局部非弹性变形快速求解器

我们提出了一种求解非线性地质力学问题的数值方法，该问题涉及沿剪切带和裂缝的局部变形。我们利用边界元方法来求解介质的准静态弹性变形，而刚塑性本构关系控制着捕捉局部变形的位移不连续 (DD) 段的行为。使用边界元素矩阵的分层近似来开发完全隐式方案。结合适当的块预处理器，这允许通过使用迭代求解器解决切线系统的解决方案来解决大问题。剪切带和拉伸断裂的起始和生长的几个二维示例说明了该技术的能力和准确性。