Development of fundamental approaches for controlling the microstructure of liquid crystal elastomers in 4D printing based on extended micropolar theory

• Applicant: Professor Dr. Wolfgang H. Müller
• Subject Area: Mechanics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 525235558

Making functional materials, whose internal microstructure reacts to external stimuli, becomes increasingly important. They open up new opportunities for multifunctional parts and machines by changing their shape and/or properties, such as color, density, conductivity, or elastic moduli. One new technology to make such dynamic structures is 4D printing. This project aims at developing fundamental approaches for the study and mathematical modeling of such materials. Despite the significant advances in the experimental and technological development of additive manufacturing, the theoretical foundation regarding the behavior of materials with a microstructure has not yet been sufficiently developed. For instance, current experiments are only based on heuristics. For the efficient development of multifunctional parts, it would be desirable to predict the precise reaction of such parts subjected to an external stimulation. In order to achieve that, it is necessary to develop mathematical models describing the behavior of materials with a microstructure, which responds to external stimuli. Ultimately, due to the smaller dependence on experiments, this leads to a more efficient development process of multifunctional parts. Therefore, a new thermodynamically sound continuum mechanic approach to the formulation and solution of problems related to elastic materials with a changing microstructure is presented. Additional state parameters that take rotational Degrees Of Freedom (DOF) of matter into account are introduced. Their evolution is based on balance relations with source terms that simulate structural changes in the material. The effectiveness of this approach will be demonstrated for 4D printed liquid crystal elastomers (LCE). For the development, several experiments of increasing complexity for LCE structures under mechanical load or exposed to thermal stimulation are defined. They are formalized into Initial Boundary Value Problems (IBVP). Reference solutions to these IBVPs are obtained experimentally. In order to define formal initial conditions for the IBVPs, the microstructural orientation within 3D printed LCE strands is also determined experimentally. In addition, analytical and numerical solutions are found using the derived set of equations. The numerical solutions will be computed by a Finite Element (FE) program implemented using the Python library FEniCS. Regarding simple IBVPs, the analytical solutions are used to verify the program. The comparison of numerical and experimental solutions to IBVPs of arbitrary complexity allows for both the determination of material parameters, and the validation of the derived continuum model. Moreover, this workflow allows to include additional DOFs in the computational model and use complex constitutive relations. The software developed within the framework of the project for solving problems of structural transformations in LCEs can subsequently be used to solve tasks not envisaged by this project.

• DFG Programme: Research Grants
• International Connection: Italy
• Cooperation Partner: Professor Dr. Victor A. Eremeyev