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Based on the meso-structured Voronoi cell model for discrete particle assembly and the derived meso-mechanically informed constitutive relations of anisotropic Cosserat continuum, thermodynamic framework of isothermal meso-mechanically informed damage-healing and plastic process for granular materials is presented. The accumulated net (effective) damage factor tensor combining both material damage and healing effects is defined in terms of the initial (undamaged) and current (damaged) elastic moduli tensors of the meso-structured Voronoi cell attributed to the material point. According to the non-negativity of thermodynamic energy dissipations, the net damage variable is separated into the two component internal state variables; i.e. the damage and healing variables, which are accumulated in terms of incremental damage and healing variables, respectively. The meso-mechanically informed macroscopic damage-healing and plastic characterization are achieved without the need to specify macroscopic phenomenological damage, healing and plastic criteria, and their evolution laws. The merit of the proposed tensorial net damage and healing variables in modeling healing effects on initial weakened elastic stiffness (i.e. initial material defects) is demonstrated in terms of their isotropic scalar forms and integrated into the continuum damage-healing mechanics. The numerical results conceptually illustrate the performance of the proposed definitions of meso-mechanically informed net damage, damage, and healing variables. The coupled damage-healing and plastic process in anisotropic Cosserat continuum for granular materials is characterized in terms of densities of thermodynamic dissipations that make effects of the damage-healing and the plastic component processes on the material failure quantitatively comparable. [ABSTRACT FROM AUTHOR]

A mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented. The proposed mixed FE is developed based on the Hu-Washizu variational principle. Translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as the independent nodal variables. The tangent stiffness matrix of the mixed FE is formulated. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect is numerically demonstrated. Patch tests are specially designed and performed to validate the mixed FE formulations. A numerical example is presented to demonstrate the performance of the mixed FE procedure in the simulation of strain softening and localisation phenomena, while without the need to specify the macroscopic phenomenological constitutive relationship and material failure model. The meso-structural mechanisms of the macroscopic failure of granular materials are detected, i.e. significant development of dissipative sliding and rolling frictions among particles in contacts, resulting in the loss of contacts. [ABSTRACT FROM AUTHOR]

The microstructures of granular materials are represented by Voronoi cells generated with a Voronoi tessellation of discrete particle assembly. A Voronoi cell model including not only the reference particle laid inside the Voronoi cell but also its intermediate neighboring particles is presented to formulate micromechanically based macroscopic constitutive relations and constitutive modular tensors of effective Cosserat continuum. The anisotropy of effective Cosserat continuum due to intrinsic characters and deformation-induced evolutions of microstructure of granular materials of the Voronoi cell is quantitatively demonstrated. The derived micromechanically informed macroscopic constitutive relation of effective Cosserat continuum reveals that the Cauchy stresses are not only constitutively related to the strains but also to the curvatures defined in Cosserat continuum, likewise, the couple stresses are not only constitutively related to the curvatures but also to the strains. The derived modular tensors are verified by comparisons of them with those given for classical isotropic Cosserat continuum and are used to identify the elastic constitutive parameters of isotropic Cosserat continuum. The micromechanically informed macroscopic damage factor tensor to characterize anisotropic material damage of effective Cosserat continuum is formulated with no need specifying macroscopic phenomenological damage criterion and damage evolution law. The principal directions and values of the derived damage factor tensor along with numerical results reveal the microscopic mechanisms of macroscopic damage phenomenon, i.e. loss of contacts, re-orientation of contacts of the reference particle with its intermediate neighboring particles and concomitant volumetirc dilatation of the Voronoi cell. [ABSTRACT FROM PUBLISHER]

In the framework of the second-order concurrent computation homogenization method for saturated granular material, meso-structured RVE (Representative Volume Element) is modeled as a compact assembly of saturated discrete particles. The boundary conditions imposed on the RVE are comprised of the two parts: (1) the boundary displacements and pressures prescribed by downscaled macroscopic strain variables and pore pressure, and (2) constrained fine scale fluctuations of mesoscopic hydro-mechanical variables expressed in terms of periodic boundary conditions. The present paper focuses on the estimation of effective hydro-mechanical material properties and constitutive behaviors of meso-structured RVE of saturated discrete particle assembly via a proposed homogenization procedure. To achieve this target, a novel scheme for determining and imposing periodic boundary conditions on peripheral particles contacting with the RVE boundary of saturated discrete particle assembly is proposed. Numerical results demonstrate performances and capabilities of the proposed scheme in estimating effective hydro-mechanical non-linear material properties and predicting hydro-mechanical constitutive behaviors of saturated granular materials evolving with loading histories. They also demonstrate the significance and necessity of imposing periodic boundary conditions on the RVE in proper prediction of effective hydro-mechanical material properties and constitutive behaviors. [ABSTRACT FROM AUTHOR]

Abstract A multiscale modeling and characterization method for coupled damage-healing-plasticity occurring in granular material is proposed. The characterization is performed on the basis of multiscale modeling of granular material in the frame of concurrent second-order computational homogenization method, in which granular material is modeled as gradient-enhanced Cosserat continuum at the macroscale. The damage-healing-plasticity is characterized in terms of meso-structural evolution of discrete particle assembly within representative volume elements (RVEs) assigned to selected local material points in macroscopic continuum, with no need to specify macroscopic phenomenological constitutive models, failure criteria along with evolution laws, and associated macroscopic material parameters. The proposed modeling and characterization method for coupled damage-healing-plasticity in granular material is comprised of the following three constituents. The incremental non-linear constitutive relation for the discrete particle assembly of RVE is first established. Then the meso-mechanically informed incremental non-linear constitutive relation of macroscopic gradient-enhanced Cosserat continuum is derived from volume averages of the RVE-scale solutions. Finally the thermodynamic framework is set up to define meso-mechanically informed anisotropic damage and healing factors, anisotropic net damage factors combining both damage and healing effects, and plastic strains. Densities of damage, plastic and total dissipative energies as well as non-dissipative healing energy, as scalar internal state variables, are provided to compare the effects of damage, healing and plasticity on material failure and structural collapse. The numerical example of strain localization and softening problem is performed to demonstrate the performance and applicability of the proposed multiscale modeling and characterization method of coupled damage-healing-plasticity for granular materials. Highlights • Propose a novel multiscale method to characterize damage-healing-plasticity. • Derive a nonlinear constitutive relation for a discrete mesostructured RVE. • Derive a nonlinear constitutive relation of gradient Cosserat continuum. • Define damage, healing, net damage factors, plastic strain in thermodynamic frame. • The effects of damage, healing and plasticity on material failure are comparable. [ABSTRACT FROM AUTHOR]

Based on the meso-structured Voronoi cell model and the meso-macro homogenization procedure between the discrete particle assembly and the porous continuum for wet granular materials, meso-hydro-mechanically informed effective pressure and effective stress measures for saturated and unsaturated porous media are defined. The meso-hydro-mechanically informed generalized effective stress for saturated porous continua taking into account the volumetric deformation of solid grains due to pore liquid pressure is derived. The Biot coefficient associated to the meso-hydro- mechanically informed generalized effective stress for saturated porous media is formulated. The differences of the definitions for proposed generalized effective stress and Biot coefficient compared with those defined in the generalized Biot theory of saturated porous continua and in averaging theories are discussed. The wet meso-structured Voronoi cell model, consisting of three immiscible and interrelated (i.e. solid grains, interstitial liquid and gas) phases, at low bulk saturation (below about 30%) is proposed. A meso-structural pattern with the binary bond mode of pendular liquid bridges is assumed in particular to derive the meso-hydro- mechanically informed macroscopic anisotropic effective pressure and effective stress tensors for unsaturated porous media. As the isotropic case of the wet meso-structured Voronoi cell model is considered, the meso-hydro-mechanically informed effective pressure tensor degrades to the scalar variable in the same form as in the theory of macroscopic unsaturated porous continua. The proposed meso-hydro-mechanically informed Bishop's parameter is derived and obtained as a function of saturation, porosity, and meso-structural parameters, without need to introduce any macroscopic phenomenological assumptions for the description of hydro-mechanical constitutive behavior. [ABSTRACT FROM AUTHOR]