Mechanical Behavior Analysis Of Granular Materials Based On Microstructural Continuum Models

Granular materials consist of a large number of discrete granular solids and their voids,which exist widely in nature and production activities.Granular materials have complex physical and mechanical properties which are closely related to their microstructural information,such as particle shape,size distribution,particle arrangement,contact relationship at a particle pair.Generally,there are two approaches to study the mechanical properties of granular materials:the discrete approach and the continuum approach.The discrete approach is closer to the physical nature of granular materials,and it can fundamentally investigate the influence of microstructural information.However,the motions of a large number of particles are quantitatively required in practical applications,which is still limited by the computational scale.Therefore,in the framework of continuum,it is still an important way to develop macroscopic continuum models with considering the microstructural information.In this thesis,the effects of the granular microstructure on macroscopic mechanical properties of granular materials on are studied.The specific contents are as follows:Firstly,in order to provide more macroscopic variables to descibe microstructural information for homogenization,a micromechanics-based micromorphic model of granular materials is proposed,and this model can consider a more complete deformation mode of granular materials.The micromorphic model decomposes the motions(translation and rotation)of particles,it considers that the micro real motion is composed of the macro(average)motion and a fluctuation between the micro and macro motions.This leads to 6 independent translational degrees of freedom and 6 independent rotational degrees of freedom in the micromorphic model.Based on this motion decomposition,the macroscopic constitutive relationships are derived represented by the microstructural information.Secondly,considering the complexity of micromorphic model,the rotational degree of freedom is restrained,and the independent rotational degrees of freedom are reduced to 3.In this model,the particle motion is also decomposed,and the macroscopic constitutive relationships are deduced based on the decomposition,and then the equilibrium equations and the motion equations are also obtained.Based on the proposed micromorphic model,the propagation behaviors of wave in elastic granular media are investigated.The dispersion phenomena are investigated for four wave types such as transverse wave,longitudinal wave,transverse shear wave and transverse rotational wave,and the frequency band gaps and wave speeds are predicted for these four waves.Then,the effects of microstructural information,including contact stiffness parameters and the internal length,on dispersion behaviors are discussed,and wave speeds of transverse wave,longitudinal wave,transverse shear wave and transverse rotational wave are discussed in detail.Thirdly,an elastoplastic constitutive model is adopted in the framework of micromorphic theory,and the corresponding codes are completed via the user element subroutine(UEL)in ABAQUS.The ability of the micromorphic elastoplastic model is verified to simulate the strain softening and strain localization behaviors.The effects of microstructural parameters such as the contact stiffness and the internal length on the macro-mechanical response of granular materials are investigated in detail.And the influence of internal friction angle and dilatancy angle on macroscopic mechanical behaviors of granular materials is also detailedly investigated.Finally,considering the high heterogeneity of granular materials,the projection scheme between macro and micro variables of particles needs to be non-affine.Based on this idea,by introducing the gradient terms and taking the dissipation at a particle group scale(a middle scale)into account,a non-affine projection scheme between macro and micro variables is established.Then,two forms of deformation free energy are established without considering the particle rolling and with considering the particle rolling.Based on the thermodynamics approach,the micromechanics-based gradient models are developed for granular materials.Through these models,numerical simulations of the strain softening and the strain localization are carried out.The effects of gradient terms,particle rolling,sample size and internal length on the macroscopic mechanical properties of particle assemblies are discussed in detail.