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

Abstract

Analyzing axisymmetric solids under torsional loading the 3d(imensional) problem can always be reduced by one dimension, since the displacement field and the rotation field are independent of the cylindrical (angle) co‐ordinate Θ, respectively. For this purpose a four‐node ring‐element for finite deformation axisymmetric and torsional problems was recently developed and is now going to be up‐dated. The original assumption of the enhanced displacement gradient H̃=αi⊗Gi is expanded in two steps according to Simo, Armero and Taylor and to Glaser and Armero, respectively: firstly in defining the additional unknowns (parameters) αi as objects in the material configuration and pushing forward H̃ by (1+U⊗Grad) ∣ξ=0—this provides ‘objectivity’—and secondly in replacing αi⊗Gi by Gi⊗αi. 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. Copyright © 2001 John Wiley & Sons, Ltd.

Direct-differentiation-based sensitivity analysis of an axisymmetric finite element formulation including torsion

“…(5), which stems from the basis variation, equals the last term in Eq. (8). The variation of the velocity gradient δL is subsequently obtained by multiplying Eq.…”

“…Finite strain formulations for generalized axisymmetry in solid mechanics have been presented in [5], and later on in various contexts like thermomechanical homogenization [6], mixed or enhanced strain formulations [7][8][9], ALE formulations [6], consolidation analysis [10], or others [11,12]. Contact mechanics in the context of generalized axisymmetry has been treated in [14], for example.…”

On strong discontinuities in anelastic solids. A finite element approach taking a frame indifferent gradient of the discontinuous displacements

“…Regarding these 'aes' (or 'aedg') formulations frame indi erent descriptions of the assumed enhanced part of the displacement gradient were carried out only recently by Glaser and Armero [9] and Celigoj [10].…”