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.
Summary
This paper presents a multiscale model based on a FEM×DEM approach, a method that couples discrete elements at the microscale and finite elements at the macroscale. FEM×DEM has proven to be an effective way to treat real‐scale engineering problems by embedding constitutive laws numerically obtained using discrete elements into a standard finite element framework. This proposed paper focuses on some numerical open issues of the method. Given the nonlinearity of the problem, Newton's method is required. The standard full Newton method is modified by adopting operators different from the consistent tangent matrix and by developing ad‐hoc solution strategies. The efficiency of several existing operators is compared, and a new and original strategy is proposed, which is shown to be numerically more efficient than the existing propositions. Furthermore, a shared memory parallelization framework using OpenMP directives is introduced. The combination of these enhancements allows to overcome the FEM×DEM computational limitations, thus making the approach competitive with classical FEM in terms of stability and computational cost.
SUMMARYIn this work, the consequences of using several different discrete element granular assemblies for the representation of the microscale structure, in the framework of multiscale modeling, have been investigated. The adopted modeling approach couples, through computational homogenization, a macroscale continuum with microscale discrete simulations. Several granular assemblies were used depending on the location in the macroscale finite element mesh. The different assemblies were prepared independently as being representative of the same material, but their geometrical differences imply slight differences in their response to mechanical loading. The role played by the micro-assemblies, with weaker macroscopic mechanical properties, on the initiation of strain localization in biaxial compression tests is demonstrated and illustrated by numerical modeling of different macroscale configurations.
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