Abstract: The tetrahedral mesh is good at building three-dimensional solid finite element discrete model because of its powerful geometric characterization, while it behaviors overly-stiff property leading to large errors, which greatly limit the widely use of the tetrahedral mesh. Since the tetrahedral mesh is an important issue in computational mechanics and is also a main focus. A new type of edge-based smoothed finite element method of tetrahedron mesh(ES-FEM-T) is extended to 3D solid mechanics visco-elastoplastic material. Numerical examples verified that computational efficiency of the ES-FEM-T is higher than the finite element method(FEM) and face-based smoothed finite element method. This method not only inherits the strong tetrahedral geometry characterization capabilities, but also improves the accuracy and efficiency of the tetrahedral mesh, which has a broad engineering application prospects.

Key words: Edge-based smoothed finite element method of tetrahedron, Meshfree method, Numerical method, Visco-elastoplastic