Jc. Simo et al., IMPROVED VERSIONS OF ASSUMED ENHANCED STRAIN TRI-LINEAR ELEMENTS FOR 3D-FINITE DEFORMATION PROBLEMS, Computer methods in applied mechanics and engineering, 110(3-4), 1993, pp. 359-386
Improved three-dimensional tri-linear elements for finite deformation
problems are developed based on an assumed enhanced strain methodology
which, in the linear regime, incorporates the classical method of inc
ompatible modes as a particular case. Three crucial modifications of a
recently proposed element, which reduces to Wilson's brick in the lin
ear regime, are introduced to prevent locking response in distorted co
nfigurations and to maintain proper rank, while preserving excellent p
erformance in bending dominated and localization problems: (i) a modif
ied quadrature rule; (ii) an additional enhancement of the divergence
term; and (iii) a modification of the isoparametric shape function der
ivatives for the three-dimensional problem. Moreover, these modified s
hape function derivatives are shown to improve the performance of the
standard tri-linear brick in distorted configurations. In addition, a
strategy is described to circumvent the memory storage requirements in
the static condensation procedure of the enhanced strain parameters.
The excellent performance of the improved methodology is illustrated i
n representative numerical simulations.