考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。

ANALYSIS OF LOCALIZED DEFORMATION IN SHEAR BAND CONSIDERING DEGRADED STIFFNESS BASED ON GRADIENT-DEPENDENT PLASTICITY

Distributed shear strain and displacement in localized shear band were investigated considering degraded stiffness in the strain-softening process based on gradient-dependent plasticity. Shear band was treated as a one-dimensional shearing problem and constitutive relation between shear stress and shear strain was bi-linear elastic and strain softening. Elastic shear strain in shear band was dependent on shear elastic modulus, damage variable and residual shear modulus. The bi-linear constitutive relation determines the total shear strain in shear band. Subtracting the elastic strain from the total strain yields the non-local plastic shear strain that depends on the flow stress and the damage variable. A yield function was proposed to consider damage in the context of classical plastic theory. The second-order shear strain gradient was introduced into the yield function. Analytical solution of the local plastic shear strain in shear band was derived and then the local plastic shear displacement was obtained by integrating the local plastic shear strain. Analytical results show that after the degraded stiffness is involved in the present model, elastic shear strain (or displacement) increases while plastic part decreases. Degraded stiffness has no influence on the stability of the system composed of shear band and elastic rock. Present analytical solutions can be simplified as earlier results without the degraded stiffness. Compared with in situ observation for localized shear deformation of rock, the validity of the proposed analytical solutionsconsidering degraded stiffness and strain gradient was verified.