基于梯度塑性理论的岩样峰后变形特征研究*

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摘要提出了单轴压缩的岩样在受到剪切破坏条件下的全部变形特征，即轴向、侧向、环向、体积应变及峰后泊松比的解析式。弹性应变采用虎克定律描述；塑性应变依赖于局部化带尺寸，由梯度塑性理论确定。在弹性及应变软化阶段，由于分别采用了线弹性及线性应变软化的本构关系，轴向应力-轴向应变曲线、轴向应力-侧向应变曲线、轴向应力-体积应变曲线及轴向应变-体积应变曲线都具有双线性特征。然而，在软化阶段，轴向应力-峰后泊松比曲线却是非线性的；峰后泊松比是变化的，可能超过0.5，这与泊松比不同。由轴向应变及侧向应变计算得到的体积应变依赖于试样的几何尺寸，因此，在软化阶段，轴向应力-体积应变曲线的斜率并非材料本构参数。以往的力学模型很难采用解析式描述全部变形特征，这充分体现了这里所采用力学模型的优越性。

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	王学滨

关键词 ：岩石力学, 应变局部化, 峰后变形, 梯度塑性理论, 轴向应变, 侧向应变, 体积应变, 峰后泊松比

Abstract：Analytical solutions of axial，lateral，circumferential and volumetric strains，and post-peak Poissons ratio of rock specimen subjected to shear failure in uniaxial compression are proposed. Hookes law is adopted to describe elastic strain. Plastic strain is determined by gradient-dependent plasticity where internal length controls the thickness of shear band. Axial stress-axial strain curve，axial stress-lateral strain curve，axial stress-volumetric strain curve and axial strain-volumetric strain curve exhibit bi-linear behaviors due to the fact that constitutive relations of linear elasticity and linear softening are utilized. However，in the strain-softening stage，the curve of axial stress and post-peak Poissons ratio is nonlinear. Different from the Poissons ratio prior to the onset of shear strain localization，the post-peak Poissons ratio changes with axial stress levels and is possibly greater than 0.5. The volumetric strain measured in experiments or calculated by the present theoretical analysis depends on axial and lateral strains，which is related to the geometrical dimensions of rock specimens. Therefore，the slope of the axial stress-volumetric strain curve in strain-softening stage cannot be taken as a constitutive parameter，which is different from that of the axial stress-pure volumetric strain curve. The pure volumetric strain is the sum of elastic volumetric strain and plastic volumetric strain that is assumed to be due to shear dilatancy in shear band. The advantage of the present mechanical model is that the whole characteristics of deformations including post-peak Poisson’s ratio，axial，lateral，circumferential and volumetric strains can be described analytically by it.

Key words： rock mechanics strain localization post-peak deformation gradient-dependent plasticity axial strain lateral strain volumetric strain post-peak Poissons ratio

引用本文:

王学滨. 基于梯度塑性理论的岩样峰后变形特征研究*[J]. 岩石力学与工程学报, 2004, 23(S1): 4292-4295.
Wang Xuebin. CHARACTERISTICS OF POST-PEAK DEFORMATIONS OF ROCK IN UNIAXIAL COMPRESSION BASED ON GRADIENT-DEPENDENT PLASTICITY. , 2004, 23(S1): 4292-4295.

链接本文:

https://rockmech.whrsm.ac.cn/CN/Y2004/V23/IS1/4292

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