Design of materials with extreme thermal expansion using a three-phase topology optimization method

We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum thermal expansion, zero thermal expansion, and negative thermal expansion. Assuming linear elasticity, it is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void. We also show that there is no mechanistic relationship between negative thermal expansion and negative Poisson's ratio.