Modeling Approach and Finite Element Analyses of a Shape Memory Epoxy-Based Material

A series of structurally related epoxy resins were prepared as model systems for the investigation of the shape memory response, tailoring their thermo-mechanical response and describing their strain evolution under triggering stimuli with a thermo-viscoelastic model. The shape memory behavior on epoxy resin was modeled through the definition of linear viscoelastic parameters, in combination with the general time-temperature reduction scheme. Specifically, this translates into the definition of a hyperelastic response enriched with a Prony series to implement time dependency and a William-Landel-Ferry (WLF) equation to implement temperature dependency. While the hyperelastic response parameters are found with a standard fitting procedure on compression tests, finding the correct parameters for the Prony series might be challenging. For this reason, an ad-hoc optimization process was coded in Mathworks Matlab environment: proper guess values are created and then a chain of constrained optimizers (such as genetic, particle swarm, pattern search and different non-linear programming algorithms) with smart evolving boundaries looks for the right set of parameters. The ability to correctly predict strain history and shape transitions with a finite element model was evaluated on a case study for self-deployment of a folded tubular structure. Tubular specimens were tested and the model was used to reproduce the switching from a temporary folded six-pointed star shape to their original cylindrical shape. Overall, this approach proved to be a very effective way to simulate complex shape memory responses in time and temperature domains, for which standard Dynamic Mechanical Analyses (DMA) and uniaxial tensile or compression tests are sufficient to calibrate material parameters for Finite Element (FE) implementation.