Abstract Mesh-sensitivity of post-localisation analysis is an inherent drawback of continuum based finite element methods. Out of many available regularisation techniques, the nonlocal method has proved to provide viable solutions. It can be implemented at the constitutive level without adjusting equilibrium equations. This study aims to apply the nonlocal theory to critical state based Nor-Sand model and evaluate its applicability to simulate drained and undrained biaxial compression tests of dense sand. The nonlocal averaging of void ratio leads to the regularisation of the state parameter. Mesh independent load–displacement curves of dense sand are obtained during both softening and at the critical state. Hence the nonlocal theory is capable of adequately regularising the post-peak dilation for both fully drained and globally undrained analysis. Along with scaling, it can be used to obtain a physically realistic force–displacement response during the shear localisation analysis of granular materials without the need for extreme mesh refinement. Finally, limitations of the nonlocal regularisation are discussed with a parametric study.

中文翻译：

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用非局部临界状态模型对排水和不排水致密砂进行后定位分析

摘要 后定位分析的网格敏感性是基于连续体的有限元方法的固有缺陷。在许多可用的正则化技术中，非局部方法已被证明提供了可行的解决方案。它可以在本构层面实施，而无需调整平衡方程。本研究旨在将非局部理论应用于基于临界状态的 Nor-Sand 模型，并评估其在模拟密砂排水和不排水双轴压缩试验中的适用性。空隙率的非局部平均导致状态参数的正则化。在软化和临界状态下都获得了密实砂的网格独立载荷-位移曲线。因此，非局部理论能够为完全排水和全局不排水分析充分调整峰后膨胀。与缩放一起，它可用于在颗粒材料的剪切定位分析期间获得物理上真实的力-位移响应，而无需极端的网格细化。最后，通过参数研究讨论了非局部正则化的局限性。