Combining dual domain material point method with molecular dynamics for thermodynamic nonequilibriums

This study presents a scalable three‐dimensional (3D) multiscale framework for continuum‐discrete modeling of granular materials. The proposed framework features rigorous coupling of a continuum‐based material point method (MPM) and a discrete approach discrete element method (DEM) to enable cross‐scale modeling of boundary value problems pertaining to granular media. It employs MPM to solve the governing equations of a macroscopic continuum domain for a boundary value problem that may undergo large deformation. The required loading‐path‐dependent constitutive responses at each material point of the MPM are provided by a DEM solution based on grain‐scale contact‐based discrete simulations that receive macroscopic information at the specific material point as boundary conditions. This hierarchical coupling enables direct dialogs between the macro and micro scales of granular media while fully harnessing the predictive advantages of both MPM and DEM at the two scales. An effective, scalable parallel scheme is further developed, based on the flat message passing interface (MPI) model, to address the computational cost of the proposed framework for 3D large‐scale simulations. We demonstrate that the proposed parallel scheme may offer up to 32X and 40X speedup in strong and weak scaling tests, respectively, significantly empowering the numerical performance and predictive capability of the proposed framework. The 3D parallelized multiscale framework is validated by an element test and a column collapse problem, before being applied to simulate the intrusion of a solid object. The multiscale simulation successfully captures the characteristic response of intrusion as postulated by the modified Archimedes' law theory. The progressive development of the stagnant zone during the intrusion is further examined from a cross‐scale perspective.

Section: Discussionmentioning

confidence: 99%

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

Liang

Zhao

et al. 2022

“…Different from most multiscale methods where homogeneous deformation is assumed within the RVE model, we adopt an RVE model that is proposed for a coupled MD–MPM technique, 34 in which the strain rate or velocity gradient is assumed uniform. This assumption is general and could be more reasonable in problems involving large deformation.…”

Section: An Adaptive Granular Rve Modelmentioning

confidence: 99%

“…Given the aforementioned problems, this work aims to improve existing granular RVE models by adapting a recently proposed RVE model 34 for molecular dynamics (MD). To overcome the distortion of the RVE box and the associated time‐consuming contact detection between boundary particles and image particles, an adaptive RVE model equipped with an evolutionary periodic boundary (EPB) algorithm is developed, by which the mentioned issues can be well resolved.…”

Section: Introductionmentioning

confidence: 99%

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

Feng

Wang

2021

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.

“…Various approaches have thus been proposed to decrease the cell‐crossing error by either using the basis functions other than the linear Lagrangian basis functions or adopting the modified gradient of basis functions for internal force calculation. Typical examples include generalized interpolation material point method (GIMP), convected particle domain interpolation (CPDI) method, and dual domain material point (DDMP) method . The MPM enhanced using quadratic and higher order B‐spline basis functions, hereafter referred to as B‐spline MPM (BSMPM), has been recently reported and attracting increasing attention .…”

Section: Introductionmentioning

confidence: 99%

A local grid refinement scheme for B‐spline material point method

Sun

Gan

Huang

et al. 2020

A local grid refinement scheme for the material point method with B-spline basis functions (BSMPM) is developed based on the concept of bridging domain approach. The fine grid is defined in the local large-deformation regions to accurately capture the complex material responses, whereas other spatial domains are discritized by coarse grids. In the overlapping domain between the fine and coarse grids, the constraint of particle displacements obtained with different grids is enforced using the Lagrange multiplier method to eliminate the spurious stress reflection at the fine/coarse grid interface. Representative numerical examples have shown that the BSMPM simulations with the proposed local grid refinement scheme could provide the solutions in good agreement with those obtained with the uniformly fine grid, and that no significant spurious stress reflection is induced at the fine/coarse grid interface, even for the bridging domain size as small as the cell size of the fine grid. It is also found that the proposed local grid refinement method can significantly reduce the BSMPM computational time compared with the cases for uniformly fine grids. A multitime-step algorithm is presented and shown to considerably enhance the efficiency of the present local grid refinement scheme with no compromise in accuracy.