FINITE ELASTOPLASTIC DEFORMATIONS OF SPACE-CURVED MEMBRANES

Under restriction of an isotropic elastic response of deformed lattice, a covariant theory of finite elastoplasticity is developed in principal axes of a pair of deformation tensors. In material description, the tenser pair consists of the plastic deformation tenser and the total deformation Cauchy-Green tenser. The proposed theory is applied to elastoplastic membranes, whose reference and current configurations can be arbitrary space-curved surfaces. Pressure-insensitive von Mises yield criterion and isotropic hardening are considered as a model problem. With a particular form of the strain energy function, given in terms of elastic principal stretches, through an explicit enforcement of the plane stress condition we arrive at a reduced two-dimensional problem representation, which is set in the membrane tangent plane. Numerical implementation details are given to show an important role of the operator split methodology in simplifying the state update computation and the computation of the consistent tangent modulus. A set of numerical examples illustrates the performance of the presented theory and indicates some of the possible areas of application.