The Research Of Deformation Gradients Effects On Granular Materials

Granular materials are assemblies composing of particles and pores,displacements of particles are strongly discontinuous and nonlinear in strain localization.The stress of material point in an assembly is not only related to the strain and loading history of the point,but also affected by the high-order deformation gradient.Therefore,this paper is based on Discrete Element Method to study the deformation gradient effect on two-dimensional granular materials,through observing the evolutions of macroscopic stress,work and the invariants of third-order stresses,the effects of first-order shear strain gradient and first-order rotation gradient on mechanical behavior responses of linear contact model and user-defined rolling resistance model can be got,the main researches of this paper are as follows:Firstly,based on the principle of virtual work,the microscope expressions of macroscopic stresses and the conjugated strains and the virtual work expressions of internal force of different continuums are derived.In this paper,a displacement controlled loading method is used to simulate the deformation of a granular assembly,displacement field is a polynomial function of macro strains.Secondly,the effects of first-order shear strain gradient on the mechanical behaviors of linear contact model are studied.The results show that:in low strain,the larger first-order shear strain gradient has little effect on the value of the macroscopic shear stress;in high strain,the larger first-order shear strain gradient has a softening effect on the macroscopic shear stress.In the whole loading process,with the first-order shear strain gradient increasing,the values of the third-order stress,the third-order work and the ratio of the third-order work versus the total work gradually increases,it shows that the contribution of the third-order work versus the total work cannot be neglected.With the first-order shear strain gradient increasing,the invariants'values of third-order stresses fluctuates more and more violently,the phenomenon of strain localization is more and more obvious and concentrated.Thirdly,the effect of first-order shear strain gradient on user-defined rolling resistance model is studied.Based on the linear contact model,the rolling friction parameter?_r is introduced to construct a user-defined rolling resistance model.The results show that:compared with the linear contact model,the variation tendencies of macroscopic shear stress,third-order stress,work,the ratio of the third-order work versus the total work and invariants of third-order stresses are basically same,but their variation degrees are different.The macroscopic shear stress,the third-order stress,the work and the invariants of third order stresses all becomes larger,the strain localization phenomenon of an assembly is more concentrated and obvious.It indicates that the first-order shear strain gradient effects on the mechanical behavior of granular material increases after considering the rotation degree of particles.The analysis shows that the softening effect of the first-order shear strain gradient on the macroscopic stress is reduced.For the two contact models,different particle radius and initial porosity will affect the softening effect.The evolution of normal contact density function reveals the reason for the change in the softening effect.With the change of anisotropy degree increasing,the change of macroscopic shear stress increases,the softening effect increases.Finally,the effect of first-order rotation gradient on the mechanical behaviors of user-defined rolling resistance model is studied.The results show that:for the same size assemblies,with the first-order rotation gradient increasing,the absolute values of the macroscopic couple stress and the third-order stresses will firstly increase and then decrease,and the values of third-order stresses are greater than that of the macroscopic couple stress.The radius and initial porosity of an assembly affect the variation tendency of the ratio of the third-order work versus the total work.However,during the whole loading process,the value of ratio is always large,which indicates that the contribution of third-order work to total work cannot be ignored.For assemblies of different sizes,the effects of first-order rotation gradient have a size effect.When the initial porosity of an assembly is relatively large,the variation tendency of the ratio varies with the size of an assembly,but the variation tendencies of macroscopic stresses will not be affected by the sample size.