磁电热弹耦合材料弹塑性断裂问题

Fracture of electro-magneto-thermo-elasto-plastic multiphase composites

在线弹性裂纹研究基础上,将热弹塑性对控制方程和边界条件的非线性影响作为伪载荷处理,使得弹塑项以伪体积力和伪面力形式出现,进而将磁电热弹耦合材料三维裂纹弹塑性问题转化为解时域超奇异积分方程问题。针对矩形裂纹,基于裂纹前沿奇性应力分析结果,通过将广义位移间断未知函数表达为基本密度函数与多项式之积,为超奇异积分方程组建立了数值方法。对典型例子进行数值计算,得到裂纹前沿广义应力的变化规律,表明将热弹塑性对控制方程和边界条件的非线性影响作为伪载荷处理是正确的。

Based on the investigation of the linear elastic crack problems,a time-domain hypersingular integral equation（TD-HIE） method was applied to solve a crack elastic-plastic problem in a three-dimensional electro-magneto-thermo-elastic coupled viscoplastic multiphase composite.Then,the crack elastic-plastic problem was reduced to solving a set of time-domain hypersingular integral equations,in which the unknown functions were the extended incremental displacement discontinuity gradients.Based on the analytical solution of singular extended stress field near the crack front,a numerical method of the TD-HIEs for a rectangular crack subjected to extended incremental loads was proposed with the extended incremental displacement discontinuity gradients approximated by the product of time-domain basic density functions and polynomials.Finally,some examples were calculated,and the extended stresses near the crack front were presented.