A micromechanical model to predict the effective thermomechanical behavior of one-way shape memory polymers

Abstract

Shape memory polymers (SMPs) are a class of intelligent materials capable of recovering their original shape in response to external stimuli. This study employs a modified Mori-Tanaka (MMT) model to predict the effective thermomechanical behavior of SMPs. By utilizing a homogenization procedure, a constitutive equation describing the evolution of the effective behavior of SMPs under thermomechanical loading was proposed. The model accounted for the SMP's dual-phase structure, consisting of active and frozen phases, and determined the effective stiffness by considering each phase's shape and volume fraction. Unlike existing phase transition models, the proposed model incorporates the interaction between phases and the phase transition process throughout the thermomechanical cycle. The model was implemented in the UMAT user subroutine of the ABAQUS software to simulate the mechanical behavior of SMPs. Investigations into various inclusion phase shapes revealed that an ellipsoidal shape most accurately represents the morphology of the inclusion phase. While shape recovery is influenced by inelastic strain, the stress response of the present model showed improved agreement with experimental results due to the consideration of phase interactions during transformation. Application of the proposed model to the auxetic behavior of a re-entrant structure fabricated from PLA demonstrated that varying Poisson's ratios and cell-opening factors (CoF) can be achieved by programming different deformation magnitudes. The most negative Poisson's ratio (−0.64) was obtained at a 70° re-entrant angle induced by a 20 mm pre-displacement. Additionally, the formulation was extended to simulate particle release, highlighting its potential application in drug delivery. The findings suggested that microstructure and non-uniform deformation significantly influence the cell-opening factor.