An Eulerian formulation for large deformations of elastically isotropic elastic-viscoplastic membranes

Typical models of membrane-like structures use a Lagrangian formulation of a hyperelastic membrane with a specified reference configuration.Here, an Eulerian formulation is proposed for modeling elastically isotropic, elastic-viscoplastic membranes.The membrane is modeled as a composite of an elastic and an inelastic component with evolution equations for elastic deformation tensors for each component.The model includes hyperelastic response as a special case and has a smooth elastic-inelastic transition capable of modeling both rate-independent and rate-dependent inelastic response.Strongly objective numerical algorithms are developed for integrating the proposed evolution equations.Also, an example of an initially flat circular membrane loaded by a follower pressure is considered to examine: rateindependent elastic and elastic-plastic responses, as well as rate-dependent inelastic relaxation effects.