岩样单轴拉伸损伤不均匀性分析——第一部分:基本理论

INHOMOGENEITY ANALYSIS OF DAMAGE UNDER UNIAXIAL TENSION (I)——BASIC THEORY

研究了损伤变量(率)的局部化特征。基于非局部理论,将损伤变量作为非局部变量,它与局部损伤变量及其二阶梯度有关。岩石的本构关系取为双线性应变软化。利用弹性区与损伤局部化区域交界处的交界条件(局部损伤变量为零)及损伤局部化区域的宽度为局部损伤变量达到最大值时所对应的宽度的假设,得到了应变软化阶段局部损伤变量、局部损伤变量率及损伤局部化区域的宽度的解析解。此外,在应变软化阶段,拉应力、拉应变及非局部损伤变量的关系与经典损伤模型在应变软化阶段的定义方式不相同,其差别在于非局部损伤变量前的系数是2而不是1。这样定义的优越性是可以保证局部损伤变量的最大值为1,意味着在损伤局部化区域的中部试样完全被拉断,与人们的常识相符。局部损伤变量在损伤局部化区域的平均值就是非局部损伤变量,而且,最大局部损伤变量是平均损伤变量的2倍。

The localization of damage variable (rate) is investigated. Based on non-local theory,the damage variable is non-local variable and is dependent on local damage variable and its second spatial gradient. After onset of damage localization,the constitutive relation is considered linear strain softening. The boundary condition between elastic and damage zones where the local damage is zero is used and the assumption that the width of damage zone is determined according to maximum local damage variable is adopted. The analytical solutions of local damage variable,local damage variable rate and width of localized damage zone at strain softening period are obtained. Besides,the presented definition on relation among tensile stress,tensile strain and non-local damage variable is different with traditional expression in that the coefficient of non-local damage variable is 2,not 1,in the presented definition. The advantage of the present definition is that when specimen is completely separated into two pieces,the maximum local damage variable can reach 1,which agrees with general knowledge. The average value of local damage variable in the rang of damage localization zone is the non-local damage variable. In addition,the maximum local damage variable is two times of the average damage variable.