This study presents an automated topology optimization framework for designing pentamode acoustic metamaterials. It provides precise control over the material effective acoustic properties while minimizing the shear modulus to achieve fluid-like behavior. The approach combines low-frequency homogenization for accurate property evaluation and the adjoint method for efficient sensitivity analysis. The Virtual Temperature Method (VTM) ensures structural connectivity and manufacturability, addressing the typical challenges of low-stiffness, high-mass-density microstructures. The framework is demonstrated through the design of a L\"uneburg lens and an acoustic invisibility cloak for underwater applications. Acoustic-elastic simulations validate the performance of both the unit cells and the complete devices. This method eliminates the need for predefined geometries, offering a flexible, reliable, and scalable alternative to conventional parametric optimization. It provides a powerful tool for the automated design of complex, anisotropic, pentamode metamaterials.
@article{arxiv.2603.00279,
title = {Topology optimization of pentamode metamaterials for underwater acoustics},
author = {Sebastiano Cominelli and Matteo Pozzi and Francesco Braghin},
journal= {arXiv preprint arXiv:2603.00279},
year = {2026}
}