(An) elastic-plastic finite element formulation of single-and multi-layered degenerated shells with application to sheet metal forming

Abstract

An incremental formulation incorporating the effect of shape change is derived for the non-steady large deformation problem with rate-independent elastic-plastic material. The kinematics of deformation during each step is considered by employing the natural converted coordinate system. From the derived formulation, finite element code is developed with a membrane element as a single-layered degenerated shell. Isotopic and normal anisotropic constitutive models are separately employed in the formulation. The membrane theory is then extended to the layered degenerated shell formulation in which the change of thickness is considered with incompressibility condition by introducing the layer model in plane stress state at each layer. In the membrane analysis, hydrostatic bulging of a circular diaphragm is analyzed with an isotopic constitutive model in order to check the validity of the present formulation and then the same process is analyzed with anisortropic constitutive model in order to study the effect of anisotropy in the bulging process. In the shell analysis, hydrostatic bulging of rectangular diaphragms is analyzed with an isotopic constitutive model. The validity of the formulations is confirmed through the comparison of the computational results with the existing experimental results. For the analysis of the general sheet metal forming process, the treatment of contact is considered employing the successive skew coordinate system. In order to investigate the effect of bending in the modeling of sheet metal forming process, three kinds of sheet metal forming processes are analyzed with the present membrane theory and shell theory ; stretching of a square diaphragm with a hemispherical punch as an example of stretch-dominant process, deep drawing of a cylindrical cup and deep drawing of a square cup from a circular blank as examples to consider the effect of bending. Then the computational results are compared between both theories as well as with the expe...