A generalized anisotropic deformation formulation for geomaterials

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 nonhomogeneous 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 corotational 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. 2 seriously degrade the accuracy of the results. To overcome this problem, several approaches have been proposed, for example: smoothed finite element methods [18], nodal integration approaches [19] and composite elements [20,21]. The composite element is a good choice for FDEM especially in the cases that re-meshing is needed for the simulation of dynamic fracture propagation problems.The basic feature of a composite element is its "assemblage" which is composed of several subelements. These sub-elements are relatively independent but work together to improve accuracy of strain calculations. Camacho and Ortiz [20] described a novel triangular element in which a sixnoded triangle is constructed from four three-noded triangles with linear displacement fields in each sub-triangle and a continuous linear strain field over the assemblage. Guo et al. [21] presented a detailed analysis of several composite triangular elements based on Camacho and Ortiz's work. They also proposed an alternative composite triangle in which the volumetric strain is assumed to be constant over the whole triangle.

Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite‐discrete element method

“…A comprehensive compilation of the FDEM methodology was presented in the first book on the subject, which was published by Wiley in 2004. Key aspects of the algorithms used in this work to resolve contact detection and contact interaction can be found in Munjiza et al, which can also be complemented by Wriggers and Udo Nackenhorst and Dostál et al Furthermore, the description of the formulation implemented to resolve the stresses inside the finite elements can be found in Munjiza et al and Lei et al…”

“…In the last decade, scientific application‐driven developments of FDEM have taken place at Los Alamos National Laboratory, enabling researchers to shift the boundaries of FDEM solutions towards more advanced alternatives, see Figure . These developments have produced a whole range of cutting edge FDEM algorithms including the following: Generalized large‐strain large‐displacements anisotropic deformation formulation through nonlocking composite finite elements incorporating multiplicative decomposition and selective integration for both elastic and inelastic (for instance plastic) behavior Smooth contact concepts.…”

“…A detailed description of the above listed solutions is beyond the scope of this paper. However, the interested reader can refer to the three books mentioned earlier and also to some of the recent publications on the subject …”

“…A comprehensive compilation of the FDEM methodology was presented in the first book on the subject, which was published by Wiley 11 in 2004. Key aspects of the algorithms used in this work to resolve contact detection and contact interaction can be found in Munjiza et al, 32 which can also be complemented by Wriggers and Udo Nackenhorst 33 and Dostál et al 34 Furthermore, the description of the formulation implemented to resolve the stresses inside the finite elements can be found in Munjiza et al 35 and Lei et al 36,37 In the last decade, scientific application-driven developments of FDEM have taken place at Los Alamos National Laboratory, enabling researchers to shift the boundaries of FDEM solutions towards more advanced alternatives, see Figure 1. These developments have produced a whole range of cutting edge FDEM algorithms including the following:…”

Variational inequality‐based framework of discontinuous deformation analysis

“…The DEM typically treats a material as an assembly of discrete particles interacting with one another through interparticle contacts and frictions and solve the Newton's equations of motion governing the particle system . In addition, the combined finite DEM,– the particle method, and the corresponding contact algorithm– have been presented. The related developments and applications of these methods can be found in monographs …”