Finite strain continuum phenomenological model describing the shape-memory effects in multi-phase semi-crystalline networks

Thermally-driven semi-crystalline polymer networks are capable to achieve both the one-way shape-memory effect and two-way shape-memory effect under stress and stress-free conditions, therefore representing an appealing class of polymers for applications requiring autonomous reversible actuation and shape changes. In these materials, the shape-memory effects are achieved by leveraging the synergistic interaction between one or more crystalline phases and the surrounding amorphous ones that are present within the network itself. The present paper introduces a general framework for the finite strain continuum phenomenological modeling of the thermo-mechanical and shape-memory behavior of multi-phase semi-crystalline polymer networks. Model formulation, including the definition of phase and control variables, kinematic assumptions, and constitutive specifications, is introduced and thoroughly discussed. Theoretical derivations are general and easily adaptable to all cross-linked systems which include two or more crystalline domains or a single crystalline phase with a wide melting range and manifest macroscopically the one-way shape-memory effect and the two-way shape-memory effect under stress and stress-free conditions. Model capabilities are validated against experimental data for copolymer networks with two different crystalline phases characterized by well-separated melting and crystallization transitions. Results demonstrate the accuracy of the proposed model in predicting all the phenomena involved and in furnishing a useful support for future material and application design purposes.