On large strain theories in sheet metal forming : general theories and numerical considerations with particular emphasis on strain analysis, non-conservative loading and plastic anisotropy

Sammanfattning: The fundamentals of continuum mechanics in large strain problems are treated and analysed. Special emphasis is directed to strain analysis in large deformation problems and a comparison between the different types of strain terms is made. In addition, the coaxial and non-coaxial strain paths are considered in the light of the polar decomposition of the deformation gradient tensor. The finite element technique as used in non-linear problems is taken up and the basis of the updated Lagrangian formulation is clarified. Non-conservative loads are treated and a method of incorporating these loads in that development of the ADINA program made here, is described. Orthotropic material models for large strain problems, based on Hill's yield criteria, have been derived for the case of numerical analysis and implemented in the ADINA program. An analysis of the bulge test is made for two different anisotropic materials using this model. Good agreement with experimental result are obtained, even for materials with an R-value of 1,98. An indication of the point of instability denoting the onset of necking is obtained directly from numerical analysis.