扩展有限元法在断裂力学相场模型中的应用

Application of X-FEM in a phase-field model for crack propagation

相场法和扩展有限元法(X-FEM)都是模拟裂纹扩展的重要手段。基于一种全新的相场中线算法将相场法和扩展有限元法的优势相结合,在捕捉复杂裂纹几何的同时利用X-FEM显式地构造出断裂面。相场中线算法的核心是构造辅助网格并连接辅助网格单元与相场等高线的交点,最终使用分段直线段生成相场中线。数值算例表明,使用XFEM及相场中线切割网格后,求解域的力-位移曲线保持不变,验证了将相场法与X-FEM方法结合的可行性。

Both phase-field and Extended Finite-Element Methods(X-FEM)are important means of simulating crack propagation.In this work,we propose combining these two approaches to utilize their individual benefits based on a novel medialaxis algorithm.Consequently,we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.The key idea of the medial-axis algorithm is to construct auxiliary mesh,connect the intersection points of the auxiliary mesh and phase-field isocontour and eventually generate medial axes which are composed of piecewise line segments.A numerical example shows the consistency of load-displacement curves before and after medial-axis based mesh cutting,which validates the feasibility of combing X-FEM and phase-field approaches.