Structural optimization of shape and topology for electro-mechanically coupled smart materials

• Applicant: Professor Dr.-Ing. Paul Steinmann
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 407523036

This is an extension proposal for an ongoing project to develop an efficient novel algorithm for combined shape and topology optimization in the field of geometrically linear and nonlinear electro-mechanically coupled smart materials. In the first phase of the project, we developed an innovative non-body conformal implicit solution approach to evaluate elastic, piezo-electric, electro-active polymers (EAPs), and electro-thermo-mechanical MEMS structures. The implicit solution approach is crucial to perform node-based shape optimization. In addition, two novel approaches have been developed to combine topology and shape optimization methods. The combined approaches allow us for the first time to take advantage of the dissimilar but complementary nature of topology and shape optimization when generating an optimized structure with an exact geometric representation starting from a simple initial configuration. The popularity and acceptance of electro-active polymers (EAPs) among the smart materials community and their application domains have increased significantly over the past two decades. EAPs demonstrate outstanding actuation capabilities, making them ideal candidates for soft robots, artificial muscles, etc. This particular class of materials responds to electric field excitation with large deformations and a change in the material behavior, however exhibiting a pronounced viscoelastic behavior. Hence, in the second phase of this project, we intend to extend the optimization framework to the area of sparsely explored material nonlinearity, i.e., viscoelastic behavior. Furthermore, EAPs are typically thin, shell-like structures, undergoing large deformation in the out-of-plane direction. By approximating them as two-dimensional structures, we are unable to simulate applications with out-of-plane deformation. Using a fully three-dimensional discretization increases the computational cost and numerical robustness is impaired due to the small size of the volume finite elements in the thickness direction. Therefore, in the next phase of the project, we will model thin EAP actuators with large out-of-plane deformation using shell finite elements. Based thereon, we will extend the optimization framework from phase one to optimize thin EAP actuators.

• DFG Programme: Research Grants