From discrete to continuum modelling of boundary value problems in geomechanics: An integrated FEM‐DEM approach

Abstract

Summary Double‐scale numerical methods constitute an effective tool for simultaneously representing the complex nature of geomaterials and treating real‐scale engineering problems such as a tunnel excavation or a pressuremetre at a reasonable numerical cost. This paper presents an approach coupling discrete elements (DEM) at the microscale with finite elements (FEM) at the macroscale. In this approach, a DEM‐based numerical constitutive law is embedded into a standard FEM formulation. In this regard, an exhaustive discussion is presented on how a 2D/3D granular assembly can be used to generate, step by step along the overall computation process, a consistent Numerically Homogenised Law. The paper also focuses on some recent developments including a comprehensive discussion of the efficiency of Newton‐like operators, the introduction of a regularisation technique at the macroscale by means of a second gradient framework, and the development of parallelisation techniques to alleviate the computational cost of the proposed approach. Some real‐scale problems taking into account the material spatial variability are illustrated, proving the numerical efficiency of the proposed approach and the benefit of a particle‐based strategy.

Mô hình hóa đa tỷ lệ bài toán địa cơ học sử dụng phương pháp kết hợp phần tử hữu hạn và phần tử rời rạc

“…Trong trường hợp này, việc xây dựng ứng xử dựa trên phương pháp số PTRR giúp thu được quy luật ứng xử σ = f (ε) của vật liệu, trong đó có thể xem xét quy luật này tương tự như một quy luật ứng xử phi tuyến với rất nhiều tham số (vị trí các hạt, mạng lưới tương tác, lực tương tác). Tính khả thi của phương pháp đã được minh chứng qua các nghiên cứu được công bố gần đây và việc áp dụng phương pháp sẽ có thể mở ra một hướng đi đầy tiềm năng cho việc mô phỏng nghiên cứu ứng xử của kết cấu, vật liệu và đặc biệt trong khuôn khổ bài toán địa cơ học trong tương lai [9][10][11][12][13][14].…”

Numerical study of the biaxial compressive strength of high strength concrete based on a yield design micromechanical approach

“…Finally, the computational advantage of the proposed model compared to a finite and discrete element models is its extremely low solver time. For example, for a uniaxial simulation, the kinematic approach takes less than a minute to converge (using a regular personal computer) whereas the latter are known to be time consuming and computationally demanding . However, the proposed yield design approach also has some limitations.…”

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

“…The computational homogenization is used to derive the constitutive relations based on the numerical responses of the DEM model at each Gauss point of FEM and periodic boundary conditions (PBC) are applied to the RVE to eliminate boundary effects. More extended applications with a similar hierarchical multiscale technique to geomechanics were reported in References 20‐25 Furthermore, Shahin et al 26 investigated the influence of RVE with different particle positions (randomness) on the FEM × DEM multiscale modeling. Liu et al 27 developed a nonlocal multiscale discrete‐continuum model based on the generalized mathematical homogenization scheme.…”