Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems (Q1912164)

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: (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. In addition, a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhancement strain parameters.