On the extension of the concept of rheological connections to a finite deformation framework using multiple natural configurations

The constitutive behaviors of materials are often modeled using a network of different rheological elements. These rheological models are mostly developed within a one-dimensional small strain framework. One of the key impediments of extending these models to a three-dimensional finite deformation setting is to determine how the different types of connections, i.e., a series and a parallel connection, are incorporated into the material models. The primary objective of this article is to develop an appropriate strategy to address this issue. We show that both the series and the parallel connection between two rheological elements can be modeled within a multiple natural configurations framework without changing or introducing new configurations. The difference in a series and a parallel connection is manifested in the ratio of the stress powers expended during the deformations of the associated rheological elements. Finite deformation version of some well-known rheological models have been used to demonstrate the utility of the proposed theory.