Hybrid stress tetrahedral elements with Allmanʹs rotational D.O.F.s

This paper presents two hybrid stress four-node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allmanʹs rotation is employed, the elements are plagued by zero-energy rotation modes which induce no strain. A modi"ed Hellinger}Reissner functional that treats the rotation and the skew symmetric stress as independent "elds is employed to formulate a stabilization scheme. Particular e!ort has been made to reduce the number of stress modes to minimum without sacri"cing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non-constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi-"eld element which, however, is not frame invariant and exhibits unsuppressed zero-energy deformation modes