Design of Materials with Extreme Elastic or Thermoelastic Properties Using Topology Optimization

Abstract

Isotropic composites with extremal elastic or thermoelastic properties are designed using a two or three-phase topology optimization method. The elastic composites are made of two different material phases and the thermoelastic composites are made of of two different material phases and a void phase. The composite microstructures are restricted to one length-scale.The topology optimization method is used to find the distribution of material phases that extremizes an objective function (e.g., shear modulus or thermal expansion coefficient) subject to constraints, such as isotropy and volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using a numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming.The design method is first used to design two-phase composites with extremal values of bulk and shear moduli. The properties of the optimal composites are quite far away from theoretical bounds which is explained by the fact that we only allow one length-scale of the microstructure. Then the design method is used to design three-phase materials with extremal thermal expansion coefficients. For this case, the obtained thermal expansion coefficients are very close to theoretical bounds. Furthermore, it is demonstrated how materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.KeywordsBulk ModulusTopology OptimizationShear ModuloTheoretical BoundThermoelastic PropertyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.