标题： $J$-积分在随机弹性介质中的应用 显示英文标题

标题： Application of $J$-Integral to a Random Elastic Medium

摘要： 本研究探讨了使用$J$积分来计算随机弹性介质的能量释放率的统计特性。 弹性模量的空间变异性被建模为一个各向同性的对数正态随机场。 在蒙特卡洛模拟的框架下，应用了一种修改后的轮廓积分来评估能量释放率的一阶和二阶统计矩。 这些结果与从势能函数计算出的能量释放率进行了比较。 比较结果显示，如果弹性模量的随机场在空间上是各向同性的，那么经典$J$积分的路径独立性对于计算平均能量释放率仍然有效。 然而，这种路径独立性并不适用于更高阶的统计矩。 模拟进一步揭示了空间变化的弹性模量的相关长度对试件能量释放率的影响。 显示英文摘要

摘要： This study investigates the use of the $J$-integral to compute the statistics of the energy release rate of a random elastic medium. The spatial variability of the elastic modulus is modeled as a homogeneous lognormal random field. Within the framework of Monte Carlo simulation, a modified contour integral is applied to evaluate the first and second statistical moments of the energy release rate. These results are compared with the energy release rate calculated from the potential energy function. The comparison shows that, if the random field of elastic modulus is homogeneous in space, the path independence of the classical $J$-integral remains valid for calculating the mean energy release rate. However, this path independence does not extend to the higher order statistical moments. The simulation further reveals the effect of the correlation length of the spatially varying elastic modulus on the energy release rate of the specimen.