Modeling and application of temperature-dependent elastic constants in continuous fiber-reinforced shape memory polymer composites

Abstract

The mechanical properties of continuous fiber-reinforced shape memory polymer composites (SMPCs) exhibit a pronounced temperature dependence. However, exiting models for elastic constants are not specifically developed for SMPCs. In this study, analytical models based on a revised Eshelby's inclusion theory are developed to predict the temperature-dependent longitudinal, transverse, and flexural moduli of SMPCs. Experimental data from the literature, covering SMPCs with various fiber volume fractions (4.32 %, 6.36 % and 12.97 %), are used to validate the proposed models. Validation results show high predictive accuracy for flexural modulus across all fiber content systems, while predictions for longitudinal and transverse moduli exhibit limitations at the high fiber contents (12.97 %). To overcome these constraints, a refined Rule of Mixtures for longitudinal modulus and a revised Chamis model for transverse modulus are introduced. Further numerical investigations on several classic micromechanical models reveal that the revised Chamis formulation effectively captures the temperature-dependent evolution of shear modulus. Furthermore, by incorporating the concept of storage strain, these analytical models are implemented into the commercial finite element software ABAQUS via the UMAT subroutine, enabling finite element simulation of SMPC shape memory cycles. The recovery stress under different constraining strain is also numerically investigated. Overall, the results demonstrate the developed model's capability to predict the temperature-dependent elastic constants and shape memory behavior of SMPCs. This framework bridges critical gaps between micromechanical theory and macroscale SMPC performance, providing a robust tool for multi-physics-coupled smart structure design.