岩样单轴拉伸应变局部化及全程应力–应变曲线

STRAIN LOCALIZATION AND COMPLETE STRESS-STRAIN CURVE OF ROCK SPECIMEN IN UNIAXIAL TENSION

基于梯度塑性理论,考虑了应变局部化,提出单轴拉伸条件下岩样全程应力–应变曲线解析解。沿试样长度方向的总应变的微分被认为由两部分构成:可恢复的弹性应变的微分和不可恢复的塑性应变的微分。根据虎克定律,弹性应变的微分依赖于应力的微分及弹性模量。塑性应变的微分与应力的微分、试样高度、软化模量及局部化带的厚度有关,局部化带的厚度由梯度塑性理论确定。根据总应变的微分等于弹性及塑性应变的微分之和这一假设,在峰后线性应变软化本构关系的情形下,得到全程应力–应变曲线的解析解。通过与De Borst及Muhlhaus基于梯度塑性理论得到的数值解对比,分别验证局部化带内部塑性应变分布解析解及内部长度对全程应力–应变曲线的影响。研究有关的本构参数(弹性模量及软化模量)及试样高度对全程应力–应变曲线的影响。

Analytical solution of complete stress-strain curve of rock specimen in uniaxial tension is proposed based on gradient-dependent plasticity considering strain localization initiated at peak strength. Differential of total strain along specimen length is composed of recoverable elastic part and unrecoverable plastic part. Differential of elastic strain is a function of differential axial stress and elastic modulus according to Hooke＇s law. However, differential plastic strain on a gauge length depends on specimen length, softening modulus, differential axial stress, and thickness of tensile localized band. The thickness iS determined by gradient-dependent plasticity where a characteristic length is included in yield function. According to the assumption ~daat differential total strain on a gauge length is the sum of differential elastic and plastic strains, analytical solution of complete stress-strain curve is derived. Compared with numerical results presented by De Borst and Muhlhaus, the analytical solution of distributed plastic strain in localization band and effect of internal length on Complete stress-strain curve are verified, respectively. Finally, influences of constitutive parameters, such as elastic and softening moduli, and specimen length on complete stress-strain curve are investigated.