A viscoelastic constitutive model for shape memory polymer composites: Micromechanical modeling, numerical implementation and application in 4D printing

In this work, a novel micromechanics-based thermo-viscoelastic constitutive model for shape memory polymer composites (SMPCs) is proposed and applied to four-dimensional (4D) printed SMPCs. The multi-branch constitutive model is used to simulate the time- and temperature-dependent mechanical behavior of the shape memory polymer matrix. According to the elastic–viscoelastic correspondence principle, the equivalent viscoelastic stiffness tensor of the composite is obtained in the micromechanics framework of energy-based effective strain theory and the Mori-Tanaka homogenization scheme, in which a two-parameter interfacial damage model is adopted to consider the displacement discontinuity and traction continuity conditions at the interface between the inclusion and the matrix. The numerical integration scheme for the three-dimensional (3D) viscoelastic constitutive model of SMPCs is presented, and the finite element application is implemented by the user material subroutine UMAT of ABAQUS. After identifying the model parameters with experimental data, the tensile stress-strain curves and stress relaxation phenomena of 4D printed unidirectional SMPCs are successfully described by theoretical simulations. Besides, theoretical simulations also adequately predict the shape memory behavior of 4D printed composites and complex members.