A multiscale phase-field approach for the optimization of 3D-printable architectured materials

• Applicants: Professor Dr.-Ing. Marc-André Keip; Andreas Krischok, Ph.D.
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 467434871

The goal of this proposed research project, outlined in what follows, is to better understand ultralight high-performance metamaterials and to improve their topology under individual load scenarios. Among candidates for periodic and porous microstructures are those with surfaces based on the solution of minimal surface problems such as the Schwarz Primitive Surface or the Gyroid.Current models that aim to employ such microstructures are still considerably inferior to classical optimized topologies that do not exhibit porous microstructures. Hence, we desire to realize printable devices with attributes that are well beyond the results both of non-porous topology optimization as well as those of recent models for cellular materials. Our goal is that printing corresponding solutions provides an alternative way of manufacturing sustainable devices with an optimal stiffness to weight ratio, as needed for orthopedic implants or lightweight materials in aviation applications and structural design. To realize repetitive microstructures with such properties, we intend to develop a model that is capable of aligning both the porosity and the topology of small cells to the state of deformation in the material. By means of that we could achieve favourable microstructures with attributes that are similar to natural materials such as human bone or wood if subjected to the particular load scenario (c.f. Fig. 1).We propose a two-scale phase-field approach based on solving the Cahn-Hilliard equation and an elastic problem both on the macro-scale and on the micro-scale to control the optimization of the surface of periodic cells and their compliance with respect to an elastic deformation. The micro-scale is governed by an FFT-based solution scheme with attractive attributes regarding computational efficiency.Our preliminary investigations of the proposed model in two dimensions exhibit attributes that are about 30% superior to classical optimized topologies. These promising results are expected to translate to the three-dimensional case and to offer room for further improvement upon the incorporation of additional open tasks that are outlined throughout the proposed work programme.

• DFG Programme: Research Grants