关键词: 梯度塑性理论, 非局部模型, 应变率, 局部化, 剪切带, 轴向响应, 应变软化, 稳定性

Abstract: Strain softening structural response of rock material in uniaxial compression is investigated analytically based on shear strain rate gradient formation. One dimensional shear strain rate gradient formation of the second order is proposed based on the non-local continuum model. Non-local plastic shear strain rate is dependent on local shear strain rate and its second spatial derivatives. The closed-form analytical solution of the local shear strain rate is straightly obtained by substitution of the non-local plastic shear strain rate into the local one in classical plastic theory, instead of differentiating the local shear strain with respect to time. Relative shear velocity along shear band is calculated by integrating the local shear strain rate. Velocity at the end of rock specimen beyond the peak compressive stress can be divided into two parts. One is elastic part described by Hooke’s law; the other is plastic part dependent on the relative shear velocity. Summing the two parts yields analytical solution of structural response for uniaxial compressive rock specimen subjected to shear failure. It is shown that sudden snap-back instability can occur as internal length parameter (or thickness of shear band) of rock material is decreased. Higher shear softening modulus, lower Poisson’s ratio or inclination angle of shear band can lead to brittle axial response. Based on analogy between specimen and pillar in mines, the brittle axial response of rock specimen means that pillars in mine will lose their stability and pillar bursts will occur. Main advantage of the present analytical process based on strain rate gradient formation is concise.

Key words: gradient-dependent plasticity, non-local continuum model, strain rate, localization, shear band, axial response, strain softening, stability