断裂相场模型的三维自适应有限元方法

A Three-Dimensional Adaptive Finite Element Method for Phase-Field Models of Fracture

发展了鲁棒的预测-校正算法,建立了断裂相场模型的三维自适应有限元分析.相场模型可以方便地处理复杂的断裂问题,避免了额外追踪裂纹路径且没有网格依赖性.然而,三维相场建模往往需要非常精细的网格,这降低了求解效率.针对该问题,基于交错求解方案发展了预测-校正网格自适应细化算法,实现了三维结构裂纹扩展的高精度分析.数值算例表明,所发展的方法能够准确合理地描述结构的裂纹扩展,同时网格可以在裂纹扩展的路径上自适应地细化.

A robust predictor-corrector algorithm was developed and a 3D adaptive finite element analysis for the fracture phase-field model was established.This model can deal with complex fracture problems conveniently,avoiding extra tracking of crack paths and without mesh-dependency.However,the 3D phase-field modeling usually requires extremely fine meshes,which brings reduction of the solving efficiency.Aimed at this problem,the predictor-corrector adaptive mesh refinement algorithm was developed based on a staggered solution scheme,to achieve high-precision analysis of crack propagation in 3D structures.Numerical examples show that,the developed method can accurately and reasonably describe crack propagation in structures,and the meshes can be adaptively refined along the crack propagation paths.