An Eulerian Formulation of a Growing Constrained Elastic-Viscoplastic Generalized Membrane

A thermomechanical generalized Cosserat membrane has no resistance to bending but it allows for deformations through the membrane’s thickness. This theory is generalized to allow for growth due to mass supply and is constrained to eliminate shear deformations but retain thickness changes. An Eulerian formulation of isothermal elastic-viscoplastic constitutive equations is developed using evolution equations for elastic dilatation and elastic distortional deformations. These evolution equations include time-dependent inelastic effects of homeostasis which cause a tendency for the elastic deformation measures to approach their homeostatic values. An important feature of the Eulerian evolution equations is that they depend only on the current state of the membrane and therefore are appropriate for modeling growth. Examples of zero-stress growth and constrained growth are considered.