DESIGN OF MATERIALS WITH EXTREME THERMAL-EXPANSION USING A 3-PHASE TOPOLOGY OPTIMIZATION METHOD

Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The compos ites are made of two different material phases and a void phase. The t opology optimization method consists in finding the distribution of ma terial phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found us ing the numerical homogenization method based on a finite-element disc retization of the base cell. The optimization problem is solved using sequential linear programming. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures are in fine agreement with rigorous bounds and the so-called Vigdergauz m icrostructures that realize the bounds. For three phases, the optimal microstructures are also compared with new rigorous bounds and again i t is shown that the method yields designed materials with thermoelasti c properties that are close to the bounds. The three-phase design meth od is illustrated by designing materials having maximum directional th ermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. 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. (C) 1997 Elsevier Science Ltd.