Abstract
The instabilities of soil specimens in laboratory or soil made geotechnical structures in field are always numerically simulated by the classical continuum mechanics-based constitutive models with finite element method. However, finite element mesh dependency problems are inevitably encountered when the strain localized failure occurs especially in the post-bifurcation regime. In this paper, an attempt is made to summarize several main numerical regularization techniques used in alleviating the mesh dependency problems, i.e., viscosity theory, nonlocal theory, high-order gradient and micropolar theory. Their fundamentals as well as the advantages and limitations are presented, based on which the combinations of two or more regularization techniques are also suggested. For all the regularization techniques, at least one implicit or explicit parameter with length scale is necessary to preserve the ellipticity of the partial differential governing equations. It is worth noting that, however, the physical meanings and their relations between the length parameters in different regularization techniques are still an open question, and need to be further studied. Therefore, the micropolar theory or its combinations with other numerical methods are promising in the future.
Highlights
Natural and artificial geotechnical structures play an essential role in our lives
This paper comprehensively summarizes the typical regularization approaches in dealing with mesh dependency in numerical finite element analysis, mainly including viscosity theory, nonlocal theory, high-gradient theory, and micropolar theory
Micropolar theory takes into account the independent micro-rotations of material points, so it has a more physical meaning than a wholly mathematical technique when compared with other regularization approaches aforementioned; It can efficiently and fully obtain the mesh-independent solutions for static problems as well as for dynamic problems; The thickness of shear band can be controlled by the length parameter as the cases it is influenced by the mean grain size in laboratory tests; when decohesion rather than frictional slip is the predominant failure mode, the regularization effect of micropolar theory is generally too weak to preserve the ellipticity of the boundary value problems
Summary
Natural and artificial geotechnical structures play an essential role in our lives. Granular soils, whether as the main construction materials or the foundation of geotechnical structures, determine, to an extent, their failure mechanisms. Sustainability 2022, 14, 2982 analyzing methods (e.g., finite difference method (FDM), finite element method (FEM), finite volume method (FVM), boundary element method (BEM), extended finite element method (X-FEM), discontinuous deformation analysis (DDA), finite cover method (FCM), Peridynamics (PD), discrete element method (DEM), smoothed particle hydrodynamics (SPH), material point method (MPM), etc., among others) have seen wide introduction in geotechnical engineering. Compared to FDM, as another numerical method to solve partial differential equations (PDEs), FEM is more adaptable to high-dimensional problems, and it is versatile for all complex and irregular geometries. The mesh-free methods have overcome many problems encountered with mesh based method, such as the mesh dependency problems of FEM They are more complex and time consuming than the conventional FEM to simulate the boundary value problems in geotechnical engineering. It is unable to cover all the numerical methods as the new and advanced numerical methods have been being consecutively developed by researchers in the world
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