Topology optimization of pentamode metamaterials for underwater acoustics

Abstract

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 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.

Figures (12)

• Figure 1: (a) target properties of the lens normalized with respect to water, (b) ideal (dashed line) and discretized (solid line) volume of the lens.
• Figure 2: (a) The unit cell used as a first guess. The black and white regions stand for the connecting supports and the free frame, respectively. These regions remain fixed during the optimization routine to ensure connectivity between neighboring cells. The gray area is the design domain. The blue and green boundaries are the source and destination of the periodic conditions, respectively; the red points represent the node fixed to the ground to prevent rigid motion. (b) Symmetries imposed on the unit cell and the primitive design domain are highlighted in orange. (c) Unit cell of the reciprocal lattice with the irreducible Brillouin zone in orange.
• Figure 3: (a) Connectivity issue of the optimized cell obtained solving problem \ref{['opt:optimization_lens']} with $\hat{r} = 0.14$. The layout has non-physical connections that cannot be manufactured. (b) Cell obtained solving problem \ref{['opt:optimization_lens_vtm']} using the Virtual Temperature Method (VTM). The layout has no connectivity issues.
• Figure 4: Optimized lens cells obtained solving problem \ref{['opt:optimization_lens_vtm']}.
• Figure 5: Left, the effective properties (normalized with respect to water) of the optimized cells shown in Fig. \ref{['fig:lens_cells']}, computed using COMSOL Multiphysics®. Right, the magnitude of the relative error between effective and target properties.