A Stabilized Linear Tetrahedral Finite Element with Face-Based Strain Reconstruction Kinematics for Nearly Incompressible Finite-Strain Hyperelasticity

Linear tetrahedral elements for nearly incompressible finite-strain hyperelasticity are often affected by volumetric locking and exhibit oscillatory stress/pressure fields. We propose a stabilized linear tetrahedral u-θ element combining mixed VMS stabilization with face-based strain reconstruction smoothed FEM (FSRS-FEM). Implemented in Abaqus/Standard through a user element, the method is assessed by patch test, Cook’s membrane bending, torsion, and contact analyses. At v 0 = 0.4995, the Cook’s membrane displacement error was approximately 0.42% relative to a refined C3D8H reference. The proposed element required approximately 1.6–2.2 times the CPU time of Abaqus C3D4H.