A constitutive level-set model for shape memory polymers and shape memory polymeric composites

Abstract

This work proposes a new constitutive model for shape memory polymers and shape memory polymeric composites under the use of level-set functions as additional variables of state. The model regards shape memory polymers as inhomogeneous bodies consisting of two different phases, an active (rubbery elastic) phase and a frozen (glassy elastic) phase. Introducing the level-set function provides the potential to describe the interface separating the two distinct phases in an implicit manner. Under proper thermodynamical arguments, an appropriate evolution equation is derived that provides the tool to describe phase transformations in shape memory polymers. Furthermore, an extended model version is developed that applies in shape memory polymeric composites by introducing two (or more) level-set functions so as to represent implicitly three (or more) material phases capturing the behavior of multi-shape memory polymers. The level-set constitutive equations are formulated in three dimensions, although the one-dimensional case is adopted and analyzed thoroughly. The reproduction of the shape memory thermomechanical cycles of polymers and polymeric composites provides validity and credibility to the current model.