Engineered Aggregates for Metamaterials

Abstract

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.

What is claimed is: 
     
         1 . An engineered aggregate comprising:
 a geometric multilayer body comprising at least an inner core surrounded by a compliant layer, wherein the inner core is formed of a core material having a high mass density relative to the compliant layer, and wherein the compliant layer is formed of a compliant material having an elastic modulus 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 of the energy wave within the engineered aggregate.   
     
     
         2 . The engineered aggregate of  claim 1 , wherein the geometric multilayer body is spherical. 
     
     
         3 . The engineered aggregate of  claim 1 , wherein the core material is selected from the group consisting of steel, tin, brass, nickel, iron, lead, gold, and tungsten carbide. 
     
     
         4 . The engineered aggregate of  claim 1 , wherein the core material has a density of at least 10000 kg/m 3 . 
     
     
         5 . The engineered aggregate of  claim 1 , wherein the compliant material is selected from the group consisting of silicon, rubber, polyethylene, polypropylene, polystyrene and nylon. 
     
     
         6 . The engineered aggregate of  claim 1 , wherein the compliant material has an elastic modulus of at least 1 GPa. 
     
     
         7 . The engineered aggregate of  claim 1 , wherein the core material is lead and the compliant material is nylon. 
     
     
         8 . The engineered aggregate of  claim 1 , further comprising at least one outer protective layer disposed atop the compliant coating. 
     
     
         9 . The engineered aggregate of  claim 1 , wherein the target frequency at which the geometric multilayer body exhibits 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, p l  is the density of the core material and w is the target frequency.