Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing

To realize negative thermal expansion (NTE), porous composites made of two materials with different coefficients of thermal expansion are being actively researched. NTE can be realized by taking advantage of the thermal deformation mechanisms of a composite material's internal geometry. However, in addition to negative thermal expansion, materials with anisotropic and large positive thermal expansion are also desirable for various applications. Also, additive manufacturing provides new ways to fabricate composites by layering multiple materials at arbitrary points in three-dimensional space. In this study, we developed a design methodology for porous composites, which showed defined thermal expansion characteristics, including negative and positive thermal expansion as well as isotropic and anisotropic thermal expansion. Our approach was tested based on the fabrication of a multi-material photopolymer by additive manufacturing. The internal geometries required to produce such characteristics were designed by topology optimization, which is the most effective structural optimization method for realizing macroscopic inward deformation and for maintaining stiffness. The designed structures were converted to three-dimensional models and fabricated by multi-material photopolymer additive manufacturing. Using laser scanning dilatometry, we measured the thermal expansion of these specimens, revealing well-ordered thermal expansion, from anisotropic positive thermal expansion to anisotropic negative thermal expansion, over a wide range of about −3 × 10⁻⁴ K⁻¹ to 1 × 10⁻³ K⁻¹.