Systems and methods for designing and fabricating multi-layer structures having thermal expansion properties

Abstract

Systems and methods for designing and fabricating multi-layer structures having thermal expansion properties are provided. One embodiment of the present invention provides a multi-layer structure. Briefly described, one such multi-layer structure comprises a central layer, a first layer, and a second layer. The first layer is constrained to a first side of the central layer and has a first thickness. The first layer comprises a first material having a first value for a thermal expansion property. The second layer is constrained to a second side of the central layer and has a second thickness. The second layer comprises a second material having a second value for a thermal expansion property. The second thickness and the second value for the thermal expansion property and the first thickness and the first value for the thermal expansion property are such that, upon a change in temperature, the net change in the strain energy in the first layer and the net change in the strain energy in the second layer are substantially equal.

1 . A system for designing multi-layer structures having thermal expansive properties, the system comprising: 
 a first portion of logic configured to define a set of variables related to materials properties of a central layer, a first layer, and a second layer in a multi-layer structure, wherein the first layer and the second layer are constrained to the central layer and the first layer and the second layer have different thickness and different coefficients of thermal expansion;    a second portion of logic configured to define, based on the set of variables related to the materials properties of the central layer, the first layer, and the second layer, a mathematical representation of the strain energy in the first layer and the strain energy in the second layer; and    a third portion of logic configured to determine one or more solutions to the mathematical representation which satisfy the condition that, upon a change in temperature, the change in strain energy in the first layer and the change in strain energy in the second layer are within a predefined variance.    
   
   
       2 . The system of  claim 1 , further comprising a fourth portion of logic configured to receive one or more design values for one or more of the variables related to the materials properties of the central layer, the first layer, and the second layer.  
   
   
       3 . The system of  claim 1 , wherein the first, second, and third portions of logic are stored in memory and further comprising a processor device configured to implement the first, second, and third portions of logic.  
   
   
       4 . The system of  claim 1 , wherein the third portion f logic is further configured to determine one or more solutions to the mathematical representation which satisfy the condition that, upon a change in temperature, the change in strain energy in the first layer and the strain energy in the second layer are substantially equal.  
   
   
       5 . The system of  claim 1 , wherein the first layer comprises a top layer constrained to the central layer and an upper layer constrained to a top side of the top layer and the second layer comprises a bottom layer constrained to the central layer and a lower layer constrained to a bottom side of the bottom layer.