二维压电材料动强度因子的扩展有限元计算

Dynamic intensity factor computation for two-dimensional piezoelectric media using an extended finite element method

采用扩展有限元求解二维弹性压电材料动断裂问题。扩展有限元的网格独立于裂纹,因此网格生成可大大地简化,且裂纹扩展时不需重构网格。采用相互作用积分技术计算动强度因子。比较了标准的力裂尖加强函数和力-电裂尖加强函数对动强度因子的影响,结果表明标准的力裂尖加强函数能有效地分析压电材料动断裂问题。分析了极化方向对动强度因子的影响。数值分析表明采用扩展有限元获得的动强度因子与其他数值方法解吻合得很好。

An extended finite element method was applied to solve dynamic fracture problems in 2D elastic piezoelectric solids.The method allowed representation of a crack independent on meshes,so mesh generation could be greatly simplified and re-meshing could be avoided as the crack grew.The dynamic intensity factors（DIFs） were computed using the contour interaction integral technique.The influences of standard mechanical crack tip enrichment functions and electro-mechanical crack tip enrichment functions on the DIFs were compared.It was shown that using standard mechanical crack tip enrichment functions is efficient to analyze the dynamic fracture problems in piezoelectric solids.The influence of poling directions on the DIFs was investigated.The DIFs obtained with the proposed method were compared with those using the other numerical methods,and remarkable agreements were observed.