  This paper explores the use of optimization to design multifunctional
metamaterials, and proposes a methodology for constructing a design envelope of
potential properties. A thermal-mechanical metamaterial, proposed by Ai and Gao
(2017), is used as the subject of the study. The properties of the metamaterial
are computed using finite element-based periodic homogenization, which is
implemented in Abaqus utilizing an open-source plugin (EasyPBC). Several
optimization problems are solved using a particle swarm-based optimization
method from the pyOpt package. A series of constrained optimization problems
are used to construct a design envelop of potential properties. The design
envelope more fully captures the potential of the metamaterial, compared with
the current practice of using parametric studies. This is because the optimizer
can change all parameters simultaneously to find the optimal design. This
demonstrates the potential of using an optimization-based approach for
designing and exploring multifunctional metamaterial properties. This proposed
approach is general and can be applied to any metamaterial design, assuming an
accurate numerical model exists to evaluate its properties.
