基于XFEM的虚构域方法用于线弹性模型中的裂纹
XFEM based fictitious domain method for linear elasticity model with crack
AI总结：
本文提出基于XFEM的虚构域方法，用于模拟弹性介质中裂纹引起的位移不连续性，通过裂纹表示方法和稳定化技术提高计算效率与鲁棒性。
摘要：
减少求解计算成本是解决裂纹识别或扩展问题的关键。为避免重新划分网格，本文提出了一种新的有限元方法，用于模拟由裂纹引起的位移不连续性。该方法基于最初用于泊松问题和斯托克斯问题的虚构域方法，适应于裂纹问题的Neumann边界条件。裂纹通过水平集函数表示。数值测试采用混合公式以强调方法的准确性及其对几何形状的鲁棒性，通过稳定化技术实现。特别地，对后者进行了理论上的inf-sup条件证明。通过模拟火山内均匀加压裂纹的现实情况，以展示该方法的应用性。
英文摘要：
Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid re-meshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for illustrating the applicability of the method.
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