Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part I: Continuum formulations Original Research Article

The present work deals with studies on viscoelastic-plasticity at finite strains. Different forms can be proposed for the combination of plasticity and viscoelasticity mechanisms. In the present work, we propose two different formulations, each of them is motivated by a distinct simple one-dimensional rheological model. These different rheological models suggest different kinematic assumptions at finite strains which in turn lead to different local governing equations issued from thermodynamically consistent frameworks. However, one of the common features characterizing the two formulations is the use of local multiplicative decompositions of the deformation gradient. Model examples issued from these formulations are proposed. They are suitable for the simulation of filled rubbers, polymers and polymeric foams. Computational aspects and numerical examples within the framework of the finite element method are addressed in detail in Part II of this work.