Finite element formulation based on incremental deformation theory for sheet metal forming of planar anisotropic materials

Abstract

An implicit approach for the incremental analysis of planar anisotropic sheet forming processes is developed based on the incremental deformation theory. The incremental deformation theory based on the minimum plastic work path enables convenient decoupling of deformation and rotation by the polar decomposition. The mathematical description of a constitutive law for the incremental deformation theory is obtained from the flow theory along the minimum plastic work path. The resulting incremental constitutive law is frame-indifferent(objective) since the materially-embedded coordinate system is employed in the theory. The formulation based on the incremental deformation theory is incorporated in the elasto-plastic and rigid-plastic finite element analysis codes. In the elasto-plastic formulation, CB(Continuum Based) shell elements are employed and the are reduced to CBR(Continuum Based Resultant) shell. The CBR shell allows large rotation and large membrane / bending strain. Finite element equation for the CBR shell was derived in the explicit form. The lamina coordinate system is taken to coincide with planar anisotropic axes. Then, planar anisotropic axes during deformation are updated using the newly developed algorithm based on polar decomposition. An iterative solving method based on incremental deformation theory is also developed for a accurate and stable stress integration. The method has been found to be successfully applicable to non-quadratic yield function. Planar anisotropy is incorporated into the formulation for sheet forming by introducing the Barlat``s stress potential to describe the deformation behavior for a more wide range of materials. In the rigid-plastic formulation, a variational formulation for membrane elements based on the incremental deformation theory is derived for the incremental analysis of nonsteady static large deformation of planar anisotropic sheet metal obeying Barlat``s strain-rate potential. By using the natural convected c...