On drilling degrees of freedom in nonlinear elasticity and a hyperelastic material description in terms of the stretch tensor. Part 2: Application to membranes

SummaryThis paper is based on the spatial theory of the title problem [1] and on a membrane model resulting from the finite rotation shell theory presented in [2]. The proposed material law in terms of Biot stresses and stretches (not assumed to be symmetric a priori) takes into account transversal isotropy and incompressibility and covers large stretches. Its parameters are determined using tension- and shear tests as well as biaxial ones known in literature. A variational principle with displacement- and drilling degrees of freedom in connection with 4- and 9-node finite elements respectively and a 8-parameter material law is taken in order to analyze (1) a tension strip, (2) a rectangular membrane under transverse dead load, (3) a circular cylindrical membrane under axial load, and (4) a circular membrane with fixed edges unter internal pressure.