The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

中文翻译：

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基于 B 样条的梯度增强微极性隐式材料点法，用于解决局部大非弹性变形


数值模拟中粘性摩擦材料的准脆性响应通常由软化塑性或连续损伤模型单独或组合表示。然而，经典模型，特别是与非相关可塑性相结合时，经常会出现不适定性和数值模拟缺乏客观性的问题。此外，当网格变形达到过高水平时，有限元方法的性能在涉及有限应变的模拟中显着降低。这对粘性摩擦材料的建模提出了挑战，因为它们倾向于经历强烈的局部变形，例如在剪切带主导的失效期间发生的变形。因此，对粘性摩擦固体的响应进行精确建模是一项艰巨的任务。为了应对这些挑战，我们提出了统一梯度增强微极连续体的质点法（MPM）的扩展，旨在分析粘性摩擦材料中的有限局部非弹性变形。采用广义梯度增强微极性连续介质公式来解决与局部化和软化材料行为相关的挑战，而 MPM 则解决过度变形引起的问题。该方法利用刚性背景网格的 B 样条公式来减轻 MPM 众所周知的单元交叉误差。为了证明该方法的性能，提出了平面应变压缩和三轴拉伸试验中砂岩局部破坏的 2D 和 3D 数值研究。与有限元结果的比较证实了该公式的适用性。 此外，还提出了该公式的有效数值实现，并且证明了额外的 MPM 特定开销可以忽略不计。