A decoupled ALE method of implicit stabilized node-based smoothed finite element and its applications to large deformation analysis

Large deformation of soil mass has been often encountered in geotechnical analysis. When the small deformation assumption-based finite element method is applied to such large deformation analysis, the computational errors can be accumulated or the computational process may be terminated due to mesh distortion. In the decoupled arbitrary Lagrangian-Euler (ALE) method with separated mesh deformation and material deformation, the updated Lagrangian (UL) step is implemented followed by the Euler step to overcome the reduced computational accuracy or the computational termination caused by mesh distortion. By combining the stabilized node-based smoothed finite element method (NsFEMstab) with the ALE method, a novel NsFEMstab-ALE method is proposed, and furthermore a dynamic placement approach of nodes for the adaptive remeshing strategy is developed. Based on a rigid footing resting on ground involving large deformation, the method of NsFEMstab-ALE is examined, and numerical results show that: (1) by applying the dynamic placement method of nodes, the mesh distortion caused by large deformation can be effectively resolved, the smooth mesh transition from fine-mesh area to coarse-mesh area can be realized, and the good element quality in the whole mesh during the entire deformation process can be guaranteed. (2) the load-displacement curves predicted by the NsFEMstab-ALE method agree well with those in the literatures, and the equivalent plastic strain contours and deformed meshes calculated by the NsFEMstab-ALE method are rational.