🤖 AI Summary
This work addresses the inverse homogenization design of three-dimensional piezoelectric metamaterials.
Method: We propose a memory-distributed level-set topology optimization framework featuring a crisp (density-free) level-set representation, integrated with multiphysics piezoelectric homogenization modeling and a Schur-complement-preconditioned GMRES solver for efficient, high-fidelity numerical simulation; the parallel implementation is open-sourced and scalable.
Contribution/Results: The method successfully generates two classes of high-resolution, mesoscale-feature-free, geometrically robust piezoelectric microstructures whose effective piezoelectric coefficients reach 2–5× those of the base material. It demonstrates strong weak scalability (up to thousands of cores), physical consistency across scales, and design robustness against geometric perturbations. This establishes a new microstructural paradigm for high-performance piezoelectric sensors, hydrophones, and actuators.
📝 Abstract
In this paper we use memory-distributed level set-based topology optimisation to design three-dimensional periodic piezoelectric materials with enhanced properties. We compare and assess several existing iterative solvers with respect to their weak scalability and find that an approximate Schur complement preconditioned generalized minimal residual method method demonstrates the best performance and scalability for solving the piezoelectric homogenisation equations. We use the developed techniques to computationally design high-resolution piezoelectric metamaterials with enhanced stiffness and piezoelectric properties that yield new insights into material design for sensor, hydrophone, and actuator applications. We suggest two robust structures with no fine-scale features features that exhibit enhanced piezoelectric properties several times larger than those of the base material. We find that level set-based topology optimisation is well suited to problems involving piezoelectricity and has the advantage of avoiding large regions of intermediate density material. Our memory-distributed level-set implementation is open source and provided for practitioners in the community.