Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems

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 incompatible modes as a particular case. Three crucial modifications of a recently proposed element, which reduces to Wilson's brick in the linear regime, are introduced to prevent locking response in distorted configurations and to maintain proper rank, while preserving excellent performance in bending dominated and localization problems: (i) a modified quadrature rule; (ii) an additional enhancement of the divergence term; and (iii) a modification of the isoparametric shape function derivatives for the three-dimensional problem. Moreover, these modified shape 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 in representative numerical simulations.