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A MODE-DEPENDENT ENERGY-BASED DAMAGE MODEL FOR PERIDYNAMICS AND ITS IMPLEMENTATION

机译:基于模式的能量依赖的周向损伤模型及其实现

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摘要

The mathematical modeling of failure mechanisms in solid materials and structures is a long standing problem. In recent years, peridynamics has been used as a theoretical basis for numerical studies of fracture initiation, evolution and propagation. In order to investigate damage phenomena numerically, suitable material and damage models have to be implemented in an efficient numerical framework. This framework should be highly parallelizable in order to cope with the computational effort due to the high spatial and, depending on the problem, temporal resolution required for high accuracy. The open-source peridynamic framework Peridigm offers a computational platform upon which new developments of the peridynamic theory can be implemented. Today, isotropic material models and a very simple damage model are implemented in Peridigm.This paper proposes three energy-based damage criteria. The implementation approach as well as the extension of Peridigm with these physically motivated models is described. The original criterion of Foster et al. is adapted for ordinary state based material. The other two criteria utilize the decomposition of peridynamic states in isotropic and deviatoric parts to account for the failure-mode dependency.The original criterion is verified by the numerical simulation of two mechanical problems. At first, a virtual double cantilever beam (DCB) experiment is performed to determine the energy release rate. This value is the fundamental material property required for the proposed criteria. Additionally, the DCB problem is then used to investigate the convergence of the numerical scheme implemented in Peridigm. In a second step, a model of a plate with a cylindrical hole under tensile loading is compared with an extended finite element method solution. Results of both numerical solutions are in good agreement. Finally, a fiber reinforced micro structure model is used to analyze the effect of the different criteria to the damage initiation and crack propagation under a more complex loading condition.
机译:固体材料和结构中破坏机制的数学建模是一个长期存在的问题。近年来,周动力学已被用作断裂起始,演化和扩展的数值研究的理论基础。为了从数量上研究损坏现象,必须在有效的数值框架中实施合适的材料和损坏模型。这个框架应该是高度可并行化的,以便应付由于高空间以及根据问题而需要高精度的时间分辨率所引起的计算工作。开源蠕动框架Peridigm提供​​了一个计算平台,可以在该平台上实现蠕动理论的新发展。如今,在Peridigm中实现了各向同性的材料模型和非常简单的损伤模型。本文提出了三种基于能量的损伤准则。描述了这些物理模型的实现方法以及Peridigm的扩展。 Foster等人的原始标准。适用于基于普通状态的材料。另外两个准则是利用各向同性和偏斜部分的周边动力学状态的分解来解释失效模式的相关性。最初的准则通过两个力学问题的数值模拟得到了验证。首先,进行虚拟双悬臂梁(DCB)实验以确定能量释放速率。该值是建议标准所需的基本材料属性。此外,然后将DCB问题用于研究在Peridigm中实现的数值方案的收敛性。在第二步中,将在拉伸载荷下具有圆柱孔的板的模型与扩展的有限元方法进行比较。两种数值解的结果吻合良好。最后,使用纤维增强的微观结构模型来分析在更复杂的载荷条件下不同准则对损伤萌生和裂纹扩展的影响。

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