Mechanical metamaterials

Negative Poisson's Ratio (NPR) materials, also known as auxetic materials, have attracted attention due to their unique behavior. When materials are compressed (stretched) along a particular axis they are most commonly observed to expand (contract) in directions orthogonal to the applied load. The property that characterizes this behavior is the Poisson's ratio which is defined as the ratio between the negative transverse and longitudinal strains. The majority of materials are characterized by a positive Poisson's ratio which is approximately 0.5 for rubber and 0.3 for glass and steel. Materials with a negative Poisson's ratio will contract (expand) in the transverse direction when compressed (stretched). This unusual behavior results in a unique feature that the material can concentrate itself under the compressive load to better resist the load. Furthermore, NPR materials also become stiffer and stronger when the amplitude of the load increases. Studies and experiments have demonstrated that auxetic materials can improve mechanical properties, including shear resistance, indentation resistance and fracture toughness, compared to conventional materials from which they are made. These auxetic materials also offer very good sound and vibration absorption and could have many potential applications to aerospace and defense areas.

Although NPR materials can exist in principle, demonstration of practical examples is relatively recent. Discovery and development of materials with NPR was first reported by Lakes in 1987. The auxetic behavior was achieved using a foam characterized by a reentrant microstructure that unfolds when stretched, causing lateral expansion and negative Poisson's ratio. Following the seminal work of Lakes,  to achieve macroscopic negative Poisson's ratios a number of geometries and mechanisms have been proposed.

Left: Experimental  images of structures with different pore shape at different levels of applied engineering strain. After instability the lateral boundaries of samples A and B bend inwards, a clear signature of negative Poisson ratio behavior. Right: Evolution of Poisson's ratio of the three structures as a function of the applied engineering strain.

A significant challenge in the fabrication of materials with auxetic properties is that it usually involves embedding structures with intricate geometries within a host matrix. As such, the manufacturing process has been a bottleneck in the practical development towards applications. However, recently we showed  that instability induced pattern switches in porous elastomeric structures characterized by an initial simple microstructures may lead to auxetic behavior. Furthermore, we showed that the hole shape provides a convenient parameter to control the compaction (quantified as change of structure planar area divided by original area) and negative Poisson’s ratio of the periodic structures. Our results demonstrate that by simply changing the shape of the holes the response of porous structure can be easily tuned and soft structures with optimal compaction can be designed. Surprisingly, we show that circular holes do not lead to optimal response and that the compaction of the system can be significantly improved through a careful design of the pore shape. Furthermore, the insights gained by performing a numerical parametric exploration serve as an important design guideline in fabricating practical materials towards applications.


  • K. Bertoldi, P.M. Reis, S. Willshaw and T. Mullin. Negative Poisson’s Ratio Behavior Induced by an Elastic Instability. Advanced Materials, 22: 361-366, 2010.
  • J.T.B. Overvelde, S. Shan  and K. Bertoldi.  Compaction Through Buckling in 2D Periodic, Soft and Porous Structures: Effect of Pore Shape. Advanced Materials, 24: 2337-2342, 2012.