Large deformation analysis of geomechanics problems by a combined rh-adaptive finite element method

Finite element analysis of large deformation problems is a major challenge in computational geomechanics, due largely to the severe mesh distortion that may occur after updating the spatial configuration of the nodal points using a conventional Updated-Lagrangian approach. There are two alternative and reasonably well-known strategies to tackle this issue of mesh distortion, viz., the r-adaptive and h-adaptive methods. The r-adaptive finite element method has been designed to eliminate possible mesh distortion by changing and optimising the locations of the nodal points without modifying the overall topology of the mesh adopted to solve a given problem. In order to obtain an accurate solution by this method a relatively fine mesh is required right from the beginning of the analysis, which potentially increases the overall analysis time. On the other hand, the h-adaptive finite element method improves the accuracy of the solution by gradually decreasing the size of the elements based on an error assessment method. However, this approach may leave the very small elements in the mesh vulnerable to distortion. To eliminate the individual drawbacks of these adaptive methods, while preserving the accuracy of the solution, a combined rh-adaptive finite element method has been developed and is presented in this paper for the analysis of sophisticated problems of geomechanics that involve large deformations and changing boundary conditions. The proposed method is designed to improve the accuracy of the solution obtained using the h-refinement strategy while successfully avoiding the mesh distortion by the use of r-adaptive refinement. It is shown that this new combination can significantly increase the efficiency of adaptive finite element methods.