基于Drucker-Prager准则的岩石弹塑性损伤本构模型研究

大多数岩石材料软化本构模型在硬化函数中引入塑性内变量来表示材料的硬化/软化性质，但并不能反映岩石微裂隙损伤对材料力学性能的影响及单轴拉伸和压缩所表现的初始屈服强度f0与屈服极限fu的差异。基于D-P准则同时考虑塑性软化及损伤软化，建立岩石类材料的弹塑性本构关系及其数值算法。塑性屈服函数采用Borja等的应力张量的硬化/软化函数，反映塑性内变量及应力状态对硬化函数的影响；由于岩石损伤软化是微裂隙扩展所导致的体积膨胀引起的，因此，提出用体积应变表征岩石损伤变量的演化，并用回映隐式积分算法编制了岩石的弹塑性损伤本构程序。对单轴压缩及拉伸荷载作用下的岩石材料试验进行数值模拟，结果表明，所提出的岩石弹塑性损伤本构模型可以较好地符合岩石材料的力学特性。

Study of elastoplastic damage constitutive model of rocks based on Drucker-Prager criterion

Hardening and softening properties of the materials is described by introducing plastic internal variables to hardening function in most softening constitutive models of rock,without considering the damage effects of micro-crack growth and different performances of initial yield strength f0 and yield limit fu between the uniaxial tensile and compressive loadings.Plastic yield criterion is used simultaneously with the damage criteria to simulate the physical behavior of rock-like materials based on D-P criterion,and elastoplastio damage constitutive model with its numerical algorithm is also proposed.Borja’s hardening/softening strain function is employed as the plastic yield function,indicating the plastic internal variables and stress states are two important factors to the hardening function.Volume expansion caused by micro-crack growth is responsible for rock damage evolution D,which can be characterized by proposed function of volumetric strain.The code of elastoplastic damage constitutive model of rock is implemented using return mapping implicit integration algorithm.The proposed model is used to uniaxial tensile and compressive tests and the results agree well with the characteristics of rock-like materials and experimental curves.