Topology optimization of pentamode metamaterials for underwater acoustics

This study presents an automated topology optimization framework for designing pentamode acoustic metamaterials. It provides precise control over the material's effective acoustic properties by minimizing the shear modulus under bulk modulus and volume fraction constraints. The approach combines low-frequency homogenization for accurate property evaluation and the adjoint method for efficient sensitivity analysis. The virtual temperature method (VTM) is used to address the typical structural connectivity and manufacturability challenges of low-stiffness, high-density microstructures. The framework is demonstrated through the design of a Lüneburg 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.