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.


In this work a unified constitutive approach for a 2D composite triangle has been developed for the Combined Finite-Discrete Element Method (FDEM) [1-3]. Since its inception the FDEM has become a tool of choice for a diverse field of practical engineering and scientific simulations[4-9]. From the very initial idea of FDEM a large strain-large displacement formulation for the finite element side of FDEM has been employed in its exact multiplicative decomposition (as opposed to co-rotational) formulation. In recent years this formulation has been generalized through the concept of the so called Munjiza material element, which enables a pragmatic engineering approach to anisotropic constitutive law formulations for both large displacements and large strains in the context of the exact decomposition-based format. This approach has been recently described in detail in the book entitled "Large Strain Finite Element Method: A Practical Course" by Munjiza et al. [10], where also some novel concepts of selective integration have been proposed and applied to a whole family of finite elements. One of the elements proposed is the composite triangle finite element in 2D. In this work, this element has been implemented into an in-house FDEM software package. Through numerical examples the generalized anisotropic capabilities of the unified constitutive approach have been demonstrated and are presented in this paper.

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