Multiscale modeling of large deformation in geomechanics

Abstract

Summary Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain‐scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small‐strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil‐pipe interaction, and soil column collapse.

A thread‐block‐wise computational framework for large‐scale hierarchical continuum‐discrete modeling of granular media

“…Increasing occupancy by decreasing register pressure results in significant performance degradation when the maximum occupancy is reached. The deep reason may be that the register usage is simply spilled into L1 and L2 caches when the compiler reduces the register pressure below the imposed limit, that is, 64 registers per thread, making the memory F I G U R E 14 Coupling scheme of MPM and DEM, after 34 [Correction added on 05 November 2020, after first online publication: Figure 14 was published in black, which caused significant loss of information and has been replaced with the colored version.] [Colour figure can be viewed at wileyonlinelibrary.com] cache overloaded.…”

“…The hierarchical multiscale coupling of MPM and DEM (MPM×DEM) has been well introduced in our previous work. 34 The critical techniques are depicted here for the completeness of the presentation. As illustrated in Figure 14, the macroscopic engineering domain is firstly discretized by a set of material points in MPM.…”

“…More recently, a hierarchical framework for multiscale modeling of granular materials has been attracting particular attention, [29][30][31][32][33][34][35] which pushes a successful marriage between DEM and the continuum-based method such as the finite element method (FEM) and the material point method (MPM). The hierarchical approach differs from the other coupling schemes such as the concurrent approach 36,37 and the two-scale FEM approach.…”

“…38,39 In the hierarchical framework, continuum boundary value problems (BVPs) can be solved by the continuum-based method at the macroscopic scale in conjunction with the homogeneous responses of representative volume elements (RVEs) that are captured by DEM instead of a conventional phenomenological constitutive relation. Specifically, DEM-simulated RVEs serve as Gaussian quadrature points or material points in the hierarchical coupling of FEM×DEM 29 or MPM×DEM, 34 respectively, bridging the micro-(discrete-grain) and macro-(continuum) scales of granular media. Notably, the hierarchical framework brings two noteworthy aspects of improvements: (1) the characteristics of a granular material can be readily modeled by the continuum-based methods with DEM-simulated RVEs taking the place of phenomenological constitutive models and (2) the domain occupied only by RVEs needs to be simulated by DEM instead of the entire domain of a granular material, thereby considerably reducing the computational cost of DEM and improving the efficiency.…”

“…The total number of running steps of each RVE can be different, which offers the flexibility of performing different loading strains on different RVEs in the possible hierarchical multiscale modeling, for example, FEM×DEM 29 or MPM×DEM. 34 For a single DEM step (or iteration), three main procedures are sequentially executed as in a general implementation of DEM: (a) updating the neighbor list, (b) computing contact forces for all contacts, and (c) integrating motion of all particles. However, in this article, these three procedures are definitely parallelized in thread blocks for running on a GPU, and their corresponding algorithms are introduced in the following sections.…”