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力学学报  2014 

M积分与夹杂/缺陷弹性模量的显式关系

DOI: 10.6052/0459-1879-13-097, PP. 87-93

Keywords: M积分,损伤力学,复杂缺陷,有效弹性模量

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Abstract:

M积分在材料构型力学中表征着缺陷自相似扩展的能量释放率,而有效弹性模量下降量在传统损伤力学中是一个具有内变量属性的损伤参数.探讨了两者之间的特定关系,以此为材料构型力学与损伤力学搭建桥梁.借助穆斯海里什维利(Muskhelishvili)复势函数方法获取无限大弹性平面含圆形夹杂的弹性场解,根据M积分的复势函数解析表达式得到M积分与夹杂弹性模量的显式表达式.随后通过有限元分析,对含复杂缺陷群的弹塑性材料进行数值模拟,结果表明内部缺陷区域的有效弹性模量下降与M积分存在着特定关系.基于此,提出利用材料构型力学中的外变量参数(M积分)来替代损伤力学中的内变量参数(弹性模量下降量)描述材料的缺陷演化.

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