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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A Computational Framework Of Three-dimensional Configurational-force-driven Brittle Crack Propagation
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A Computational Framework Of Three-dimensional Configurational-force-driven Brittle Crack Propagation

机译：三维结构力驱动脆性裂纹扩展的计算框架

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摘要

We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element-based computational framework for propagation of cracks in three-dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality in the sense of Coleman's method. Consequently, the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. In a consistent way with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The crucial step for the success of this procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We propose a staggered solution procedure that results in a sequence of positive definite discrete sub-problems with successively decreasing overall stiffness, providing a robust algorithmic setting in the postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations.
机译：我们考虑准静态脆性断裂的变分形式，并为裂缝在三维物体中的传播建立了一个新的基于有限元的计算框架。我们概述了一个一致的热力学框架，用于在弹性固体中扩展裂纹，并通过利用科尔曼方法意义上的全局克劳修斯-普朗克不等式，证明了弹性平衡响应以及局部裂纹演化都遵循自然格式。因此，与经典格里菲斯准则相关的裂纹扩展方向由材料构型力确定，该材料构型力使裂纹前沿的局部耗散最大。通过使用有限元进行标准空间离散化，可以在数值上实现变分公式化，从而可以用构型节点力得出整体耗散的离散公式。因此，在空间离散的有限元环境中裂纹扩展的本构设置自然与典型的有限元网格的离散节点有关。与基于节点的设置一致，不断发展的裂纹不连续性的离散化是通过将关键节点和网格的界面面加倍来实现的。该程序成功的关键步骤是将其嵌入到一个基于r的裂纹面重新定向程序，该程序基于基于构形力的指标并结合裂纹前沿约束。我们提出了一个交错的求解过程，该过程导致一系列正定离散子问题，这些子问题的整体刚度将逐渐降低，从而在后临界范围内提供了可靠的算法设置。通过代表性的数值模拟证明了所提出配方的预测能力。

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