Constitutive modeling of SMA SMP multifunctional high performance smart adaptiveshape memory composite

Abstract

Materials design involving the thermomechanical constitutive modeling of shape memoryalloy (SMA) and shape memory polymer (SMP) composites is a key topic in thedevelopment of smart adaptive shape memory composites (SASMC). In this work, aconstitutive model for SASMC is developed. First, a one-dimensional SMA model, whichcan simulate the pseudoelastic (PE) and shape memory effects (SME) is presented.Subsequently, a one-dimensional SMP model able to reproduce the SME is addressed. BothSMA and SMP models are based on a single internal state variable, namely themartensite fraction and the frozen fraction, which can be expressed as a function oftemperature. A consistent form of the analytical solution for the SMP model is obtainedusing the fourth-order Runge–Kutta method. Finally, the SASMC constitutivemodel is proposed, following two analytical homogenization approaches. Oneapproach is based on an equivalent inclusion method and the other approachis the rule of mixtures. The SMA and SMP constitutive models are validatedindependently with experimental results. However, the validation of the composite modelis performed using the two homogenization approaches and a close agreementin results is observed. Results regarding the isothermal and thermomechanicalstress–strain responses are analyzed as a function of SMA volume fraction. Further, it isconcluded that the proposed composite model is able to reproduce consistentlythe overall composite response by taking into consideration not only the phasetransformations, variable modulus and transformation stresses in SMA but alsothe variable modulus, the evolution of stored strain and thermal strain in theSMP.