A simplified finite-strain constitutive model for SMP to simulate foldable and auxetic structures: Experiments and numerical implementation in ABAQUS

Abstract Thermo-mechanical one-way shape memory polymers (SMPs) are innovative materials capable of memorizing and recovering predefined shapes upon heating, with applications in aerospace and biomedical devices. Accurate modeling of their response to thermal and physical loads is essential for these applications. We present a simple and efficient modeling framework for polyurethane-based SMP. We conducted tensile tests at both high and low temperatures to measure the stress-strain behavior of the polymer in its rubbery and glassy phases, respectively. A thermomechanical SMP cycle leading to strain recovery was performed on a rectangular strip and an auxetic structure. To capture the shape memory effect, we extended the uniaxial frozen-phase model to a three-dimensional isotropic constitutive model based on Hencky’s law of elasticity, enabling predictions of finite-strain multi-axial loading responses. Young’s moduli for frozen and active phases were calibrated using tensile test data. The temperature-dependent phase function was established based on the shape recovery curve from thermomechanical experiments.A consistent tangent stiffness matrix was developed, and a numerical algorithm was implemented in displacement-based Finite Element (FE) software. The algorithm's capability was validated by simulating SMP thermomechanical cycles in ABAQUS and comparing results with experimental data and MATLAB code under uniaxial loading. Additionally, we performed numerical simulations of SMP thermomechanical loading on an auxetic lattice structure and compared these with experimental results. Finally, the model was used for a parametric study on a single fold structure, a building block for self-deployable or origami-inspired structures in aerospace applications. This framework streamlines the design and implementation of complex SMP structures in finite element analysis.