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 constitutive law is then incorporated in an
elasto-plastic finite element analysis code.
In the elasto-plastic formulation, continuum based resultant (CBR) shell element is employed. The CBR shell allows large rotation and
large membrane/bending strain. The laminar coordinate system is taken to coincide with planar anisotropic material axes. Then, planar
anisotropic axes during deformation are updated using a newly developed algorithm based on the polar decomposition. An iterative solving
method based on the incremental deformation theory is also developed for an accurate and stable stress integration. The planar anisotropy is
incorporated into the formulation for sheet forming by introducing non-quadratic Barlat's yield function.
For verification purposes, two examples have been simulated and compared with experimental results. The good verification results show
that the present elasto-plastic formulation for planar anisotropic sheet materials can provide a good theoretical basis for more extended
analyses of sheet forming processes.