Mechanical metamaterials

In plain language

Most materials behave the way they do because of what they are made from. A mechanical metamaterial is different: it is built from a repeating pattern of tiny structures, and the shape of that pattern decides how the whole piece bends, stretches or squashes. Two pieces made of the same plastic can behave very differently if their internal geometry is changed.

Some of these designs do unusual things. In 1987, Rod Lakes reported a foam that gets wider when it is pulled, which is the opposite of what ordinary foam does. Newer work has used high-resolution 3D printing to build lattices that are very light but still stiff. The field is active, but most examples are still small test samples made in research laboratories.

Technical explanation

The effective stiffness and Poisson's ratio of a metamaterial depend on its geometry, including the arrangement of struts, hinges and cells. A negative Poisson's ratio, sometimes called auxetic behaviour, means that a material expands sideways when stretched. Lakes produced a polyester-based foam with this property by compressing conventional foam in three directions and heating it, so that the cells were permanently reshaped. Specimens compressed by a factor of about 1.4 to 4 showed negative Poisson's ratios in that study.

A review by Bertoldi, Vitelli, Christensen and van Hecke (2017) groups newer designs into linear and mechanism-based metamaterials, including origami- and kirigami-based structures, designs that rely on instabilities and frustration, shape-morphing systems, and topological metamaterials. Their common theme is that the response comes from the way the structure is laid out and how its parts move relative to one another.

A pentamode material is an extreme case in which the ratio of bulk modulus (resistance to volume change) to shear modulus (resistance to shape change) is very large, so the material resists being squeezed far more than it resists being sheared, almost like a fluid in shear. Kadic and colleagues (2012) estimated, using calculations calibrated against fabricated three-dimensional microstructures, that this ratio could realistically reach about 1000 with current lithography. Zheng and colleagues (2014) reported ultralight lattices made by projection microstereolithography whose stiffness per unit mass remained nearly constant at very low density.

What the evidence says

Each statement is typed by the strength of its evidence and linked to the source that supports it.

Limitations and open problems

• Most reported examples are small samples made in research laboratories, and the sources reviewed here did not give verified production volumes or costs.
• Pentamode behaviour in the 2012 study depends on how closely lithography can reproduce the designed geometry, so fabrication accuracy limits the achievable performance.
• Lattices built from very fine structures can be fragile or unevenly stiff when made at scale, and the sources reviewed do not give durability data for real-world use.
• Many designs depend on fine geometric features that are hard to make with conventional manufacturing, which limits use to niche processes such as microstereolithography.

Possible future uses

Product concepts: Seismic vibration-absorbing panel

Timeline

1. 1987Rod Lakes reports a foam with a negative Poisson's ratio in Science. Sources: [1]
2. May 2012Kadic and colleagues publish a study in Applied Physics Letters on the practicability of pentamode metamaterials, estimating a bulk-to-shear modulus ratio of about 1000. Sources: [4]
3. Jun 2014Zheng and colleagues report ultralight, ultrastiff micro-architected lattices in Science. Sources: [3]
4. Oct 2017Bertoldi and colleagues publish a review of flexible mechanical metamaterials in Nature Reviews Materials. Sources: [2]

Futures this could help bring about

How far away?

A space elevator

Science unproven · 2 of 9 steps done

How far away?

Living in a spinning space habitat

Science demonstrated · 2 of 7 steps done

Related breakthroughs

• Preprint: graph-based design tool tunes 3D woven lattices for stiffness and stretch (18 Jul 2025)

Glossary

Metamaterial

A material whose properties come mainly from a designed structure, usually repeated at a scale smaller than the object it forms.

Poisson's ratio

The ratio of sideways shrinking to lengthwise stretching when a material is pulled. A negative value means the material gets wider when stretched.

Bulk modulus

A measure of how strongly a material resists being compressed evenly from all sides.

Pentamode material

An idealised material that resists compression strongly but resists shearing very weakly, so it behaves like a fluid in shear.

Sources

1. peer reviewed paper
   Foam structures with a negative Poisson's ratio
   Rod Lakes. Science, 1987. DOI: 10.1126/science.235.4792.1038. Accessed 21 Oct 2026.
2. review article
   Flexible mechanical metamaterials
   K. Bertoldi, V. Vitelli, J. Christensen et al.. Nature Reviews Materials, Oct 2017. DOI: 10.1038/natrevmats.2017.66. Accessed 21 Oct 2026.
3. peer reviewed paper
   Ultralight, ultrastiff mechanical metamaterials
   Xiaoyu Zheng, Howon Lee, Todd H. Weisgraber et al.. Science, Jun 2014. DOI: 10.1126/science.1252291. Accessed 21 Oct 2026.
4. peer reviewed paper
   On the practicability of pentamode mechanical metamaterials
   Muamer Kadic, Bückmann, Stenger et al.. Applied Physics Letters, May 2012. DOI: 10.1063/1.4709436. Accessed 21 Oct 2026.

Revision history

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