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A space-time finite element method for the modeling of dynamic fracture in elastic materials with cohesive zones.

机译：一种时空有限元方法，用于模拟具有内聚区的弹性材料中的动态断裂。

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A space-time finite element method for the solution of dynamic fracture problems in elastic materials is presented. The approach is based on a space-time discontinuous Galerkin formulation of a linear elastodynamic problem with a moving surface of discontinuity. The space-time discontinuous Galerkin method has the advantage of being unconditionally stable and allowing for the use of unstructured meshes in space-time domain. The latter feature facilitates the tracking of moving boundaries.; To test the effectiveness of the space-time discontinuous Galerkin method, the approach is first applied to the solution of a model problem, in which a solid-solid phase transition boundary is allowed to dynamically propagate along a one dimensional linear elastic bi-material bar. Since the moving interface and fracture problems are similar not only in containing moving boundaries, but also in the fact that the driving force of the interface movement and crack extension can both be interpreted as an energy release rate, the approach was extended to the solution of elastodynamic fracture problems.; Numerical results have been obtained for a moving interface problem with prescribed interface velocity and then compared with its exact solution. It is shown in this thesis that space-time finite element methods based on a discontinuous Galerkin formulation are very effective in the study of dynamic solid-solid phase transitions. Numerical results were also obtained for several two-dimensional dynamic fracture problems in elastic media with and without a cohesive zone. These numerical results were compared with various numerical as well as analytical solutions from the literature. The effectiveness of the space-time finite element method developed in this thesis is clearly demonstrated.
机译：提出了一种时空有限元方法来求解弹性材料中的动态断裂问题。该方法基于具有运动不连续表面的线性弹性动力学问题的时空不连续Galerkin公式。时空不连续Galerkin方法具有无条件稳定的优点，并允许在时空域中使用非结构化网格。后一个功能有助于跟踪移动边界。为了测试时空不连续Galerkin方法的有效性，该方法首先应用于模型问题的解决方案，在该模型问题中，允许固-固相变边界沿一维线性弹性双材料棒动态传播。 。由于运动界面和断裂问题不仅在包含运动边界方面相似，而且由于界面运动的驱动力和裂纹扩展都可以解释为能量释放速率，因此该方法扩展为弹性动力断裂问题。对于具有预定界面速度的运动界面问题，已经获得了数值结果，然后将其与精确解进行了比较。本文表明，基于不连续伽勒金公式的时空有限元方法在研究动态固-固相变方面非常有效。在有和没有内聚区的弹性介质中，对于几个二维动态断裂问题也获得了数值结果。将这些数值结果与文献中的各种数值以及解析解进行了比较。清楚地证明了本文开发的时空有限元方法的有效性。

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