Axisymmetric quadrilateral elements for large deformation hyperelastic analysis

In this paper, axisymmetric 8-node and 9-node quadrilateral elements for large deformation hyperelastic analysis are devised. To alleviate the volumetric locking which may be encountered in nearly incompressible materials, a volumetric enhanced assumed strain (EAS) mode is incorporated in the eight-node and nine-node uniformly reduced-integrated (URI) elements. To control the compatible spurious zero energy mode in the 9-node element, a stabilization matrix is attained by using a hybrid-strain formulation and, after some simplification, the matrix can be programmed in the element subroutine without resorting to numerical integration. Numerical examples show the relative efficacy of the proposed elements and other popular eight-node elements. In view of the constraint index count, the two elements are analogous to the Q8/3P and Q9/3P elements based on the u–p hybrid/mixed formulation. However, the former elements are more straight forward than the latter elements in both formulation and programming implementation.