An improved assumed enhanced displacement gradient ring-element for finite deformation axisymmetric and torsional problems

Analyzing axisymmetric solids under torsional loading the 3d(imensional) problem can always be reduced by one dimension, since the displacement eld and the rotation eld are independent of the cylindrical (angle) co-ordinate , respectively. For this purpose a four-node ring-element for nite deformation axisymmetric and torsional problems was recently developed and is now going to be up-dated. The original assumption of the enhanced displacement gradient ~H =Qi Gi is expanded in two steps according to Simo, Armero and Taylor and to Glaser and Armero, respectively: rstly in de ning the additional unknowns (parameters) Qi as objects in the material con guration and pushing forward ~H by (1 + u Grad)j^=0|this provides `objectivityʹ|and secondly in replacing Qi Gi by Gi Qi . Numerical results of three classical benchmarks, the in-plane torsion test, the copper rod impact and the thermomechanical localization of a rectangular strip are presented.