基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

A VISCOELASTIC-VISCOPLASTIC CONSTITUTIVE EQUATION OF ROCK BASED ON IRREVERSIBLE INTRNAL STATE VARIABLE THERMODYNAMICS

岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。

The viscoelastic and viscoplastic deformations of geo-materials are time-dependent energy dissipation behaviors. Within the framework of Rice irreversible internal state variable thermodynamics, two sets of internal state variables are introduced to describe structural rearrangement within solids during viscoelastic and viscoplastic deformation processes, respectively. The specific complementary energy function and the kinetic functons of internal state variables are presented, and the viscoelastic-viscoplastic constitutive equations are derived. The proposed viscoelastic constitutive equation has universality and can contain constitutive equations from classical viscoelastic models, such as the Kelvin-Voigt model and Poynting-Thomson model. The opinion that the linearity relationship between thermodynamic force and stress is the essential reason that the component model is linear is presented. The hardening effect of viscoplastic deformation can also be described accurately by the viscoplastic constitutive equation. A uniaxial creep test of an analogue material used to model geo-materials is conducted by loading and unloading paths. This method can separate viscoelastic and viscopalstic deformations in creep process. Then parameter identification is conducted through test data. Comparison between test data and theoretical curves indicates that the proposed constitutive equation can describe the creep behavior accurately, and can be a fundamental basis for forecasting and evaluating the long-term stability and analyzing the reinforcement of geo-material projects.