An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis

Abstract

The hierarchical multiscale analysis normally utilizes a microscopic representative volume element (RVE) model to capture path/history‐dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box, unless a proper reinitialization is applied. This work develops an adaptive RVE model in conjunction with an evolutionary periodic boundary (EPB) algorithm for hierarchical multiscale analysis of granular materials undergoing large deformation based on a recent RVE model proposed for coupling molecular dynamics and the material point method. The proposed adaptive RVE model avoids the reinitialization of the RVE box that even undergoes extremely large shear deformation; meanwhile, it accounts for the deformation history of the RVE model and treats the interaction between boundary particles and other image particles in a more efficient way. Numerical examples with extremely large deformation are used to illustrate the adaptive granular RVE model enhanced by the proposed EPB algorithm. Furthermore, some key features of this new methodology are further discussed for clarification.

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

“…This treatment unavoidably results in the loss of material loading history and introduces inaccuracy to some extends. It is noted that some effort have been make recently to address such issue, for example, using a rotating framework of reference and developing an adaptive RVE with evolutionary periodic boundary 64‐66 . It would be encouraging to incorporate these attempts into the proposed approach to further advance the multiscale modeling of granular media.…”

Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling

“…FEM) can be computed without resorting to phenomenological assumptions. The constitutive relation required at each Gauss point is approximated with particle-scale discrete element modelling (DEM) of a representative volume element (RVE) Zhao, 2014, 2016a;Qu et al, 2021c). A boundary value problem (BVP) simulated with FEM normally incorporates many Gauss points, thus massive DEM models need to be concurrently solved, resulting in extremely high computational costs.…”

A novel method for generating random fiber distributions for fiber-reinforced materials

“…Thus, a suitable algorithm for generating the RVE model plays a crucial role in the subsequent study to predict the elastic modulus. New algorithms, such as Random Microstructure Generation (RMG) by Melro et al, 14 Hard-Core Optimization Algorithm (HCOA) by Liu et al, 15 and an adaptive RVE model based on molecular dynamics and evolutionary periodic boundary algorithms by Qu et al 16 However, all of these aforementioned algorithms were too complex and difficult to promote.…”