Study On The Particles Breakage And Damage-Healing-plasticity Characterization For Granular Materials Based On Multiscale Approach

Granular materials are characterized as high heterogeneity and discontinuous media consisting of lots of particles and voids at the meso-scale.They exist widely in engineering practices,such as soil,geo-structure and concrete etc.Granular materials possess the discrete nature at the meso-scale,and their mechanical behavior is highly nonlinear and dissipative.The study on the complex mechanical behavior of granular materials has attracted comprehensive attention of researchers working in many different fields.The continuum model using numerical methods such as finite element method(FEM)has been widely utilized to solve the initial and boundary value problems presented in many engineering practices,but it requires phenomenological constitutive relation and material failure model,as well as a number of material parameters which have no distinct physical meaning and are even difficult to determine.In view of shortcomings of the continuum model,the discrete particle model using the discrete element method(DEM)has attracted more attentions and been developed rapidly.It has also been widely utilized to analyze and simulate the failure behavior of granular materials.However,as the discrete particle model is utilized on its own to solve the initial and boundary value problem of granular structures in the engineering practice,especially when the particle breakage is taken into account,the number of particles will increase sharply in the discrete particle model,and increasing huge number of particles will be involved in the DEM simulation.One will face to suffer from the difficulties due to high computational cost and storage space required.The computational multi-scale methodology which combines the continuum model at the macro-scale and the discrete particle model at meso-scale will make full use of the advantages of both the continuum and the discrete particle models and circumvent their respective shortcomings.It can be classified into two categories:hierarchical and concurrent computational multi-scale methods.Each discrete particle in granular materials possesses independent translational and rotational degrees of freedom.In addition,not only contact forces but also contact moments are exerted on a particle via the points on the particle surface,contacting with its neighboring particles.Form the point view of linkage of the meso and macro scales,adoption of the Cosserat continuum model,in which independent rotational degrees of freedom and couple stress are defined and introduced at each local material point,at the macro-scale is a reasonable and logical choice.The present work is performed in the the framework of concurrent computational multi-scale method and is composed of the two parts,i.e.(1)to develoed numerical models and methods for the simulation of particle breakage and to study its influence on the bearing capacity of granular material and structure;(2)to propose a characterization method of coupled damage-healing-plasticity in macroscopic continuum based on the evolution of meso-structure and the mesoscopic mechanical response of granular materials.In the first part of the work of this paper,the crushable discrete element model(CDEM),in which the two crushing models consisting of the crushing criteria and the fracture modes are proposed for an individual particle,is developed.In the proposed crushing criteria,not only the contact force but also contact moments,which are exerted on the each individual particle via the contacting points on the particle surface,are taken into account.The stress measures responsible for a particle fracture contain the average Cauchy stress and the average couple stress,exerted on a crushable particle modeled as Cosserat continuum.The breakage of an individual particle is governed by crushing criteria.The two crushing criteria are proposed in this paper.The first proposed criterion is the extension of the crushing criterion presented by Ben-Num and Einav to the Cosserat continuum.The second proposed criterion is based on the Drucker-Prager model along with the modified Cam-clay model for elastoplastic failure of soil.In the proposed two crushing criteria,one should first distinguish whether the particle is subjected to an arbitrary set of contact forces and contact moments or an isotropic/nearly isotropic set of contact forces.The fracture mode is proposed to specify how an individual crushing particle is replaced by a set of small fragments,once a certain crushing criterion is met.The number and sizes of postcrushing fragments and the arrangement of their positions,are determined according to the positions of the crushing particle and its immediate neighboring particles.The scheme to specify the fracture mode is designed so that the mass conservation of the crushing particle is ensured after it is replaced by a number of fragments,in addition,neither fictitious overlaps among the fragments nor fictitious overlaps of the fragments with the immediate neighboring particles of the crushing parent particle are introduced.In the second part of the work of this paper,the crushable discrete element method(CDEM),in which particle breakage is taken into account,is developed within two concurrent computational multi-scale methods,i.e.the bridging scale method and computational homogenization method respectively.In the bridging scale method for granular materials,the Cosserat continuum model using the FEM is applied to the whole computational domain(the FEM domain),the crushable discrete particle assembly model using the CDEM is developed and applied only to the particularly focused local region(the CDEM domain)of the whole computational domain.In the concurrent second-order computational homogenization method using gradient-enhanced Cosserat continuum at the macro-scale for granular materials,the solution procedure for the RVE subjected to the non-uniform macroscopic strain field with evolving meso-structure of crushable discrete particle assembly is developed.The volume averages of the solutions of crushable DEM are upscaled from the RVE scale of crushable discrete particle assembly to the macroscopic scale of the gradient Cosserat continuum.The third part of the work of this paper is devoted to the development of the damage-healing-plasticity characterization method in macroscopic continuum based on the meso-structure and the mesoscopic mechanical response of granular material in the framework of concurrent second-order computational homogenization method.In the framework of concurrent second-order computational homogenization,the DEM solutions are obtained for the representation volume element(RVE)subjected to the non-uniform displacement boundary condition downscaled from the macroscale in light of the generalized Hill's lemma derived for the gradient Cosserat continuum so that the satisfaction of the Hill-Mandel energy equivalence condition is ensured.The volume averages of DEM solutions of the RVE at the current incremental step can be determined and upscaled the incremental form of stress-strain constitutive relation and the total stress to the local material point,to which the RVE is assigned,in the macroscopic gradient Cosserat continuum.However,some internal state variables such as anisotropic tensorial damage factors,would not be simply obtained and upscaled by volume averages of the DEM solutions of the RVE.In this paper,the meso-mechanically informed characterization method of damage-healing-plasticity in macroscopic gradient-enhanced Cosserate continuum is developed in the framework of concurrent second-order computational homogenization.The proposed characterization method is comprised of three constituents.At first,the incremental non-linear constitutive relation for discrete particle assembly of RVE is established,then the meso-mechanically informed incremental non-linear constitutive relation of macroscopic gradient-enhanced Cosserat continuum is determined from volume averages of the RVE-scale DEM solution,at last,anisotropic damage and healing factors in the tensorial form,anisotropic net damage factors combining both damage and healing effects,plastic strains are defined in the thermodynamic framework for gradient-enhanced Cosserat continuum.Further,the densities of damage,plastic and total dissipative energies as well as non-dissipative healing energy,as scale internal state variables,are defined to compare the effects of damage,healing and plasticity on materials failure and structure collapse.The results of numerical simulations performed for the strain localization and softening example problems demonstrate the validity of the proposed fracture modes and the effect of particle breakage on material failure and structure collapse;the effectiveness and applicability of the proposed multi-scale modeling and characterization method of coupled damage-healing-plasticity for granular materials.