High Bulk Modulus Pentamodes: the Three-Dimensional Metal Water

Sound travels through water in a way that is distinct from how it moves through solids. In a liquid like water, the material resists being squeezed but offers almost no resistance to being sheared or slid sideways; it flows easily. In a solid metal, the material resists both. For decades, scientists have tried to build artificial structures that mimic the behavior of liquids but are made of solid materials. These structures, known as metamaterials, are engineered with tiny, repeating patterns that give them properties not found in nature. The goal has long been to create a solid that acts exactly like water when sound waves pass through it—a material that is stiff enough to hold its shape but soft enough to let sound flow through it as if it were a liquid. This is particularly important for underwater technology, where controlling sound is essential for communication and navigation.

The challenge lies in a physical contradiction. To act like water, a material needs to be very hard to compress (high bulk modulus) but very easy to slide (low shear modulus). Most existing solid designs that try to mimic water fail because they are either too soft to be useful or too stiff to let sound pass through correctly. They often fall short of the acoustic properties of real water by a significant margin, making them poor substitutes for the real thing. Researchers have been working on this problem for years, trying to find a geometric shape for the tiny building blocks of these materials that could solve this balance.

A team of researchers at Politecnico di Milano has now proposed a solution that they describe as the first metamaterial that fully deserves the name "3D metal water." They have designed a three-dimensional structure made of metal that, in the low frequency regime, behaves acoustically in a way that is indistinguishable from water. The key to their success was realizing that the shapes previously used to build these materials were fundamentally limited. For years, the standard design relied on links shaped like double cones—two cones joined at their narrow tips. While these shapes worked well in two-dimensional models, the researchers found that in three dimensions, they could not achieve the necessary stiffness without becoming too heavy or too rigid. The thin tips required to make the material flexible also made it too weak to resist compression, preventing it from matching the density and sound speed of water.

To overcome this, the team abandoned the double-cone shape and looked to a different kind of mechanical behavior: the way ropes work. They proposed a new design where the connecting links in the structure are not single solid rods, but bundles of many thin, parallel fibers. In a rope, the individual fibers can slide past one another when the rope is bent, which makes the whole bundle very flexible to bending forces. However, when the rope is pulled straight, all the fibers work together to resist the pull, making it very strong. By applying this principle to their metal lattice, the researchers created links that are incredibly stiff against compression but almost completely free to slide sideways. This specific combination allows the material to maintain the high resistance to compression needed to match water, while keeping the resistance to sliding so low that the material behaves like a fluid.

The researchers used computer simulations to test this new design, confirming that it could achieve a bulk modulus two orders of magnitude higher than previous attempts, finally reaching the level of real water in the low frequency regime. They also found that the structure creates a specific gap in how it handles certain types of vibrations, effectively blocking shear waves while allowing pressure waves to pass. This means that sound travels through their metal structure just as it does through water, without the unwanted distortions that usually occur in solid materials. While the design is currently a theoretical model and a computer simulation, the results suggest that it is possible to manufacture a solid that truly acts as a liquid. This breakthrough opens the door to creating advanced acoustic devices, such as lenses or cloaks, that can manipulate sound waves in three dimensions with a precision that was previously impossible.