A generalized anisotropic deformation formulation for geomaterials

TL;DR

This paper introduces a new 2D FDEM-based formulation for modeling anisotropic geomaterials, allowing detailed anisotropic property specification and avoiding common numerical issues like locking.

Contribution

The paper develops a generalized anisotropic deformation formulation using a multiplicative decomposition approach within FDEM, enhancing modeling flexibility and accuracy for non-homogeneous, anisotropic geomaterials.

Findings

Successfully models anisotropic properties with cell-by-cell variation

Avoids volumetric and shear locking issues

Applicable to various finite element types

Abstract

In this paper, the Combined Finite-Discrete Element Method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the co-rotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed.