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Regularization of continuum damage mechanics models for 3-D brittle materials using implicit gradient enhancement
Computers and Geotechnics ( IF 5.3 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.compgeo.2020.103505
S. Mondal , L.M. Olsen-Kettle , L. Gross

Abstract A well-known problem which arises in local damage models is that they suffer from mesh dependence and strain localization. In this study, we employ the non-local implicit gradient damage formulation for mesh sensitivity analysis of brittle materials. The basic concept of the non-local implicit gradient model is that the strain at a given point depends not only on the strain at that point but also on the nearby strain field. The local equivalent strain is replaced with a non-local equivalent strain, which is constructed by solving a system of partial differential equations (PDEs). We solve this system of PDEs using finite element method (FEM) and split-operator method which has been applied to 3-D microplane damage models. We extend this approach to continuum damage models and apply it to brittle material for three different loading experiments. In these examples, we demonstrate that the implementation of the implicit gradient damage model using the split-operator method can successfully be applied to complex, 3-D geometries requiring large-scale unstructured FEM meshes, and eliminate mesh dependence. In not all cases the simulations were able to obtain the desired fracture widths as this would require meshes at even smaller resolutions which is beyond our current computing capacity.

中文翻译:

使用隐式梯度增强对 3-D 脆性材料的连续损伤力学模型进行正则化

摘要 局部损伤模型中出现的一个众所周知的问题是它们受到网格依赖和应变局部化的影响。在本研究中,我们采用非局部隐式梯度损伤公式对脆性材料进行网格敏感性分析。非局部隐式梯度模型的基本概念是给定点的应变不仅取决于该点的应变,还取决于附近的应变场。局部等效应变替换为非局部等效应变,该应变是通过求解偏微分方程 (PDE) 系统构建的。我们使用有限元方法 (FEM) 和已应用于 3-D 微平面损伤模型的拆分算子方法来求解该 PDE 系统。我们将此方法扩展到连续损伤模型,并将其应用于脆性材料以进行三个不同的加载实验。在这些示例中,我们证明了使用 split-operator 方法实现的隐式梯度损伤模型可以成功地应用于需要大规模非结构化 FEM 网格的复杂 3-D 几何,并消除网格依赖性。在并非所有情况下,模拟都能够获得所需的裂缝宽度,因为这将需要更小的分辨率的网格,这超出了我们当前的计算能力。
更新日期:2020-06-01
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