Co-authors​ :

 Siddhesh KULKARNI (UNITED ARAB EMIRATES), Aoun HUSSAIN , Kamran KHAN  

Thermo-mechanical one-way shape memory polymers (SMPs) have emerged as versatile materials with a unique quality that enables them to memorize and recover predefined shapes upon exposure to heat, albeit only in one direction. These materials find applications across a broad spectrum, from aerospace applications such as deployable structures to biomedical devices like stents. With recent advancements in 4D printing, there is a growing interest in additively manufacturing intricate designs of lattice structures made of SMP. To accurately simulate the functionality of these devices constructed from such materials, it is imperative to model their inherent response to external thermal and physical loads. The type of FE simulation and the desired accuracy determine the complexity of the constitutive model. We intend to present a simple modeling framework that is faster to calibrate and easier to implement for SMP cellular solid designs in finite element codes.
To investigate SMP behavior, we chose polyurethane-based SMP named MP-4510 to conduct experimental tests. We began by conducting tensile tests at high and low temperatures to quantify the stress-strain behavior of the polymer in the rubbery and glassy phases, respectively. We proceeded with performing a free strain recovery thermomechanical cycle. In this cycle, the polymer was first subjected to tensile deformation at high temperature and then cooled to low temperature at constant load. After the polymer was unloaded to a temporary shape, it was then heated at a slow rate, causing the polymer to revert to its original shape. To capture the shape memory effect demonstrated in these tests, we employed the established frozen phase model that was originally proposed to capture uniaxial loading conditions and extended it to predict three-dimensional multi-axial loading response. However, the Young’s modulus for the frozen and active phases in the model are calibrated using the tensile tests of the polymer at glassy and rubbery phases, respectively. The temperature-dependent phase function is established and calibrated in MATLAB based on the shape recovery curve of the thermomechanical experiment. Subsequently, a consistent tangent stiffness matrix for three-dimensional isotropic modeling of shape memory polymer is formulated with a numerical algorithm for small deformation gradients and thermo-mechanical SMP problems. The capability of the algorithm is verified by simulating SMP thermomechanical cycles in ABAQUS, with the simulation results validated against the experimental data and verified using MATLAB code under uniaxial loading. Finally, a numerical simulation of SMP thermomechanical loading on an auxetic lattice structure in ABAQUS is presented, and a complete shape memory cycle response is successfully demonstrated.