Engineered aggregates for metamaterials
Materials and methods for implementing engineered aggregates in metamaterials are provided. The engineered aggregates may be tuned to oscillate resonantly under the influence of an external force improving the dynamic performance of the metamaterial by impeding dynamic excitation. The engineered aggregate generally comprise a multilayer resonant structure having at least a relatively heavy inner core surrounded by at least a compliant coating layer. The geometry and stiffness of the relative layers can be tuned to engineer a desired resonant frequency response within the aggregate for a chosen frequency range. The engineered aggregates are disposed in a matrix material to form a metamaterial. The engineered aggregates may be disposed within a mortar matrix to form a concrete metamaterial suitable for use, for example, in structural applications, including bunkers, shelters, etc.
1. A structural metamaterial comprising:
a matrix formed of a cement compatible mortar matrix material having a matrix density; and
a plurality of engineered aggregates each formed of a geometric multilayer body disposed within the matrix material, each geometric multilayer body comprising at least an inner core surrounded by at least one polymeric compliant layer, wherein the inner core is formed of a metallic core material having a core density of at least 7000 kg/m 3 and selected from the group consisting of steel, tin, brass, nickel, iron, lead, gold, and tungsten carbide, and wherein the compliant layer is formed of at least one compliant material selected from the group consisting of silicone, rubber, polyethylene, polypropylene, polystyrene, nylon, and urea formaldehyde, and having a compliant layer density that is lower than both the matrix density and the core density, and an elastic modulus that is less than both the matrix elastic modulus and the core elastic modulus and at least 10 −1 GPa, adapted to induce a kinetic oscillation in the inner core when exposed to an energy wave that imparts mechanical energy to the geometric multilayer body within at least one target frequency range, such that the engineered aggregate exhibits a negative effective mass to trap at least a portion of the mechanical energy within the engineered aggregate such that the stress experienced by the surrounding matrix material is reduced; and
wherein the plurality of engineered aggregates are randomly disposed within the matrix in a mixture.
2. The metamaterial of claim 1 , wherein the plurality of engineered aggregates are spherical.
3. The metamaterial of claim 1 , wherein the core material is lead.
4. The metamaterial of claim 1 , wherein the core material has a density of at least 10000 kg/m 3 .
5. The metamaterial of claim 1 , wherein the compliant material is urea polyurethane.
6. The metamaterial of claim 1 , wherein the compliant material has an elastic modulus of at least 1 GPa.
7. The metamaterial of claim 1 , wherein the core material is lead, the matrix material is mortar, and the compliant material is nylon.
8. The metamaterial of claim 1 , further comprising at least one outer protective layer disposed atop the compliant coating.
9. The metamaterial of claim 1 , wherein the target frequency at which each of the geometric multilayer bodies exhibit negative effective mass is dependent on the elastic modulus of the compliant material and the size of the geometric multilayer body in accordance with the following expression:
ω
2
=
3
2
E
s
R
l
t
ρ
l
where E s is the elastic modulus of the compliant material, R l is the radius of the inner core, t is the thickness of the compliant layer, ρ l is the density of the core material and co is the target frequency.
10. The metamaterial of claim 1 , wherein at least two different types of engineered aggregates are disposed within the matrix, each type of engineered aggregate being adapted to induce a kinetic oscillation in the inner cores at a different target frequency range.
11. The metamaterial of claim 1 , wherein the concentration of plurality of engineered aggregates disposed within the matrix is at saturation.
12. The metamaterial of claim 1 , wherein the plurality of engineered aggregates are adapted to induce a kinetic oscillation at a target frequency characteristic of at least one energy wave type selected from the group consisting of seismic waves, blast waves, and aircraft vibration waves.