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: rate-independent elastic
and elastic-plastic responses, as well as rate-dependent inelastic relaxation
effects.
Keywords
Eulerian formulation, elastic-viscoplastic, membranes,
large deformations, smooth elastic-inelastic transition
