A computational inverse problem approach for the design of morphing processes in thermally activated smart structural materials

Abstract

Shape memory polymers (SMP) are attracting increasing attention as a class of smart structural materials due to their light weight, ability to exhibit variable stiffness and undergo large deformations without damage, and, of course, their shape memory effect. SMP have the clear potential to be used to develop a variety of structures that are intrinsically morphable. In theory, a structure composed completely of SMP could have limitless shape-changing functionality, provided sufficient activation and mechanical actuation. Towards the utilization of this potential functionality, this work presents a computational framework to design the optimal activation and actuation to morph a structure composed of a smart material into a predefined shape or set of shapes. A numerical study is shown for the example of thermally activated smart materials in which the objective is to identify the applied boundary heat and traction to deform and lock a given structure into a predefined shape with minimal total energy and without damaging the material. The finite element method is used to analyze the response of the structure given a set of design parameters, and a nonlinear optimization algorithm is applied to identify the ideal activation and actuation to achieve the desired deformation. Through an example problem based on thermally activated SMP, the approach is shown to provide a generalized means to optimally design and/or control smart material structures. The key challenges of this approach are addressed, and the foundation is laid for further exploration into computational approaches for the solution of similar coupled multi-physics inverse problems.