Instability and failure of particulate materials caused by rolling of non-spherical particles

摘要

In particulate materials under compression at the peak load the accumulated damage allows particle rolling.For non-spherical particles the moment equilibrium dictates that further increase in displacement requires reduced shear stress producing an effect of apparent negative stiffness; its value depends upon the magnitude of the compressive stress.Dilatancy produced by rolling particles reduces the value negative stiffness,while the contraction phase causes immediate instability.Material with rolling particles is macroscopically modelled as a matrix containing inclusions with negative shear modulus.When the concentration of negative stiffness inclusions is low,the effective shear modulus is positive and the material is stable.When the concentration reaches a critical level the effective shear modulus abruptly becomes negative and the material loses stability.Furthermore,there exists a special value of negative shear modulus of inclusions (and hence the magnitude of compressive stress) when the critical concentration becomes zero,such that the first rolling particle induces the global instability.