Mechanics of soft active materials with phase evolution

This paper studies the mechanics of soft active materials where the actuation is generated due to the formation of phases that are stress-free at the moment of their creation and therefore experience no deformation in the associated configuration. Phase formation is a continuous time-dependent process, which results in individual phases forming at different times and in different configurations of the material body, and thus it is coupled with mechanical deformation. Subsequent deformation of the material body results in individual phases experiencing different states of deformation and the overall material response results from the combined responses of the individual phases weighted by their respective volume fractions. Therefore, a great challenge in modeling the mechanics of soft active materials with evolving phases is to track the deformation and evolution of individual phases formed at different times and in different configurations. In this paper, a generalized one-dimensional model framework is presented to address this challenge. However, this model proves to be computationally inefficient. In response, an effective phase model is developed that tracks the combined deformation histories of new phases through a single, effective deformation. Both the general and effective phase models are evaluated with two fundamentally distinct phase evolution rules for three common mechanical problems: extension, stress relaxation, and creep. The first evolution rule represents a discrete transition from one phase to another while the second rule corresponds to a general transition from several phases into one phase. The effective phase model demonstrates excellent agreement with the generalized theory for all three mechanical problems considered under both types of evolution rules.