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 modelled as gradient-enhanced Cosserat continuum at the macroscale, meanwhile modeled as a discrete particle assembly at the meso-scale. 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 together with evolution laws, and associated macroscopic material parameters.

The concurrent computational homogenization method achieves a two-way coupling between the meso- and macro-scales by transiting information downscaling and upscaling, and solving the boundary value problems defined at the macroscale and the meso-scale simultaneously with a nested solution scheme.

The boundary conditions for a RVE simulation are extracted from downscaled deformation response of the macroscopic continuum of granular materials in light of the derived generalized Hill’s lemma and are further discretized to impose them to all of the peripheral particles of discrete particle assembly of RVE via their contacting points with the material outside the RVE.

The incremental non-linear constitutive relation for the discrete particle assembly of RVE is established. With given incremental translational and angular displacements prescribed on the peripheral particles of the RVE, incremental forces and couple moments applied to the peripheral particles on the RVE boundary are expressed in terms of the elastic stiffness of the current deformed meso-structure of the discrete particle assembly of RVE and the incremental dissipative frictional forces condensed to the peripheral particles of the RVE.

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 characterize 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.

Key words: Multiscale modeling and characterization, Damage-healing-plasticity, Granular materials, Concurrent computational homogenization, Gradient Cosserat continuum, Discrete particle assembly

Professor Xikui Li is a professor of computational mechanics working for Department of Engineering Mechanics, Dalian University of Technology. He is the member of Scientific Committee of International Research Center for Computational Mechanics founded in 2016 at Dalian University of Technology. He serves as a member on the Editorial Boards of Int. J. Numerical Methods Eng. and Int. J. Damage Mechanics. He studied Computational Mechanics in Swansea with Prof O. C. Zienkiewicz and obtained his PhD at the University Wales of Swansea, UK. He was also an ARC (Australia Research Council) Int Fellow at University of Newcastle (2006). He worked as the Guest Editor of Special Issue “Damage Mechanics in China” of Int. J. Damage Mechanics (Vol.19(7) and Vol.19(8)). He also served as vice-Chairman (1999-2003, 2007/11), Chairman (2003/07) of Academic Committee of Solid Mechanics of China. He was Director of Division of “Structures, Architectures and Environments”, Expert Panel Committee of the National Science Foundation of China (NSFC) (2000/01).

He was conferred the “APACM Award for Senior Scientists” in 2010 and the "ICACM Fellows Award" in 2013. He was conferred “2016 Highly Commented Paper Award – Literati Award” of Journal of “Engineering Computations” for the chapter “Multiscale hydro-mechanical analysis of unsaturated granular materials using bridging scale method” by Emerald Group Publishing Limited

He has published over 200 journal papers. He presented as the first paper the mathematical model and its FE solution procedures for deforming porous media interacted with multi-phase pore fluid flows. The developed model was successively applied to oil industry and civil Engineering. The model has also been extended to include the thermal and chemical effects with mixed FE procedure. His research interests cover many areas of computational mechanics, and recently meso-macro computational multi-scale methods for discrete particle assembly - Cosserat continuum modeling of granular materials.