A Locking-Free Face-Based S-FEM via Averaging Nodal Pressure using 4-Nodes Tetrahedrons for 3D Explicit Dynamics and Quasi-statics

Abstract

A locking-free face-based S-FEM, combined with the Averaging Nodal Pressure (ANP) technique, is proposed to solve explicit dynamics of geometric nonlinear nearly-incompressible solids, using simplest linear tetrahedral elements (FS-FEM/ANP-T4). An explicit Adaptive Dynamic Relaxation (ADR) technique is also implemented for the analysis of quasi-static problems. Our studies have found that the proposed method has better accuracy and convergence compared to the standard FEM with ANP (FEM/ANP) and previous selective face-based and Node-based S-FEM (FS/NS-FEM). With the ADR, proposed method can reach the nonlinear quasi-static response much faster than the conventional explicit dynamic relaxation. No temporal instability is observed in FS-FEM/ANP-T4 in large deformation case. In addition, FS-FEM/ANP-T4 also equips the robustness against mesh distortion as FS/NS-FEM but uses less computational time. It has also been applied to solve a practical 3D problem, a rubber hanger for the car exhaust system. FS-FEM/ANP-T4 can be considered as an excellent numerical method other than FS/NS-FEM for simulating rubber-like materials.