Steady State Of Mixed Finite Element Theory And Its Application In The Material Forming

A two-dimensional stabilized, mixed finite element formulation for viscoplastic and superplastic flow problem is studied in this thesis. With this algorithm, the distribution and variety regularity of the mechanics parameters in the material can be determined when the material is subjected to working load. By modeling the forming of the material in computer, the products' designer can predict the forming results and make modifications correspondingly before actual process is done.Under high temperature forming condition, metal material undergoes a large plastic deformation, sometimes they even present a superplastic behavior. To this high non-linear problem, solution by normal FEM will lead to big error or even wrong result. The volume's approximate incompressible feature is considered in this thesis and introduced to velocity field as restraint, then a new displacement-pressure mixed FEM is formulated. Finite element formulations for four viscoplastic and superplastic constitutive models are derived respectively and corresponding FORTRAN codes are written.In this thesis, the development of the numerical simulation methods in plastic forming and the classic plastic FEM theories are reviewed first; Then four viscoplastic and superplastic constitutive models and the mixed FEM algorithm that is adopted in this thesis are described in detail; Last, some examples are tested by the mixed FE program and the efficiency of the algorithms is verified in comparison with ANSYS result.