Mechanical Metamaterials, Elastic Metamaterials

Rod Lakes University of Wisconsin

negative Poisson ratio     Poisson article     thermal expansion     negative stiffness     elastic chirality     viscoelasticity     structural hierarchy

    Metamaterials are materials in which structure and composition allows unusual properties such as negative values of physical properties, or extreme values of physical properties; meta means beyond or superior. Our materials developments predate such parlance by more than 30 years. Mechanical properties such as elasticity, viscoelasticity, and thermo-elasticity are emphasized, so materials of interest to us may be called elastic metamaterials or mechanical metamaterials. Electromagnetic materials such as those used to control waves for super-lenses and cloaking are in another class. We have not thus far worked with electromagnetic wave control materials.
Recently rib lattices comprised of slender bars or ribs (also called truss lattices) have been called truss metamaterials.

Poisson's ratio
    The first 3D materials with a negative Poisson's ratio are foam materials that can have Poisson's ratio as small as -0.8. They have been referred to as anti-rubber, as dilational and as auxetic. The cause of the negative Poisson's ratio in this case is non-affine deformation. One may also achieve a Poisson's ratio of -1 by a two-dimensionally chiral honeycomb structure.

Thermal expansion
    We develop the first material microstructures which can exhibit coefficients of thermal expansion larger than that of either constituent. The expansion can be arbitrarily large positive or arbitrarily large negative, or zero. These materials substantially exceed the bounds for thermal expansion of a two-phase composite. They contain considerable void space. We present dense extremal materials with void space tending to zero. by allowing slip at interfaces between phases.

Negative stiffness
    We develop the first composite materials with inclusions of negative stiffness which attain extreme viscoelastic behavior and exceed conventional bounds. Extremely large Young's modulus exceeding the modulus of diamond has been attained. These composites contain inclusions capable of phase transformations. The transformation is partially constrained by the surrounding matrix. High damping can also be achieved in lumped systems in which negative stiffness heterogeneity is on a larger, even a macroscopic, scale. Recently, materials with stored energy or sources of power have been called active materials.

Elastic chirality
    Chirality is well known in chemistry, optics, biology, and geology, however classical elasticity cannot accommodate chirality. We develop the theoretical framework to understand elastic chirality and to interpret experiments. We design and make the first 2D chiral elastic material. We design and make via 3D printing the first 3D printed Cosserat chiral elastic material. These may be called chiral metamaterials.
Recently we show that a stiff surface lattice exhibits elastic chirality. We also show chiral elastic solids can exhibit extreme Poisson's ratios.

    We attain high stiffness combined with high viscoelastic damping by proper choice of material microstructure and constituent properties, as demonstrated by experiment. Practical damping layers based on this concept are possible.

Strength to density ratio
    We attain a high ratio of strength to weight in cellular materials and structures with structural hierarchy. Honeycombs and foams with hierarchical structure give rise to much improved strength for given density. Gustave Eiffel used structural hierarchy for large scale structures; James Clerk Maxwell used structural hierarchy in analyses. Our contribution was to use composite theory to demonstrate the strength advantage of hierarchical honeycombs, foams, and lattices, and to confirm with experiment.

    We attain giant piezoelectric properties; even approach singular values of properties, by several methods. Methods may be applied on different length scales. See Negative stiffness inclusions

Cosserat elasticity
    Strongly Cosserat elastic solids offer freedom not present in classically elastic solids. We design and make Cosserat solids. Stress concentration factors are reduced, and there is a pathway to greater toughness.