SUMMARYIn this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu-Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional material models can be implemented without additional assumptions.

SUMMARYIn this paper we address the extension of a recently proposed reduced integration eight-node solid-shell finite element to large deformations. The element requires only one integration point within the shell plane and at least two integration points over the thickness. The possibility to choose arbitrarily many Gauss points over the shell thickness enables a realistic and efficient modeling of the non-linear material behavior. Only one enhanced degree-of-freedom is needed to avoid volumetric and Poisson thickness locking. One key point of the formulation is the Taylor expansion of the inverse Jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes. The transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept. Further crucial points are the Taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the Taylor expansion of the second Piola-Kirchhoff stress tensor with respect to the normal through the center of the element.

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This contribution deals with the application of a new solid-shell finite element based on reduced integration with hourglass stabilization in the field of sheet metal forming. The formulation includes the enhanced assumed strain (EAS) concept getting by with a minimum of enhanced degrees-of-freedom to overcome the volumetric locking and Poisson's thickness locking. To circumvent further the well-known effects of curvature thickness locking and transverse shear locking present in standard eight-node hexahedral finite elements the assumed natural strain (ANS) concept is applied. The implementation of the latter key feature is not straight-forward in reduced integration solid-shells. The second crucial point is a combined Taylor expansion of the compatible Green-Lagrange strain tensor with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization. Due to the three-dimensional modeling of the structure fully three-dimensional materials can be implemented without additional assumptions. Furthermore simulations of double-side contact problems (e.g. sheet metal forming) benefit from an exact modeling of the sheet thickness.