Does the classical solid-shell element with the assumed natural strain method satisfy the three-dimensional patch test for arbitrary geometry?

In the present study, the ability of the classical solid-shell element to satisfy the membrane patch test is examined. Theoretical and numerical investigations showed that the classical solid-shell element fails to satisfy the membrane patch test when the elements' referential covariant base vectors in the thickness directions are coordinate-dependent. This deficiency has motivated the development of a new solid-shell formulation in the present study for modeling elastic thin structures and shell-like applications. Within the new solid-shell element, a modified Green-Lagrange strain tensor is constructed by adopting both the assumed natural inhomogeneous strain (ANIS) and the enhanced assumed strain (EAS) methods. The developed formulation is implemented in the commercial finite element software Abaqus for numerical simulations. An extensive numerical study is carried out for testing the accuracy of the developed finite element. To this end, the accuracy of the ANIS solid-shell element incorporating the proposed set of 21 EAS parameters is compared to the classical ANS solid-shell element with the same set of the EAS parameters. It is shown that the ANIS solid-shell element combined with the set of 21 EAS parameters is of great accuracy and excellent performance considering both the linear and the non-linear regimes.