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This work presents a general unified theory for coupled nonlinear elastic andinelastic deformations of curved thin shells. The coupling is based on amultiplicative decomposition of the surface deformation gradient. Thekinematics of this decomposition is examined in detail. In particular, thedependency of various kinematical quantities, such as area change andcurvature, on the elastic and inelastic strains is discussed. This is essentialfor the development of general constitutive models. In order to fully explorethe coupling between elastic and different inelastic deformations, the surfacebalance laws for mass, momentum, energy and entropy are examined in the contextof the multiplicative decomposition. Based on the second law of thermodynamics,the general constitutive relations are then derived. Two cases are considered:Independent inelastic strains, and inelastic strains that are functions oftemperature and concentration. The constitutive relations are illustrated byseveral nonlinear examples on growth, chemical swelling, thermoelasticity,viscoelasticity and elastoplasticity of shells. The formulation is fullyexpressed in curvilinear coordinates leading to compact and elegant expressionsfor the kinematics, balance laws and constitutive relations.

international journal of solids and structures

The multiplicative deformation split for shells with application to  growth, chemical swelling, thermoelasticity, viscoelasticity and  elastoplasticity