  Although recent developments in 3D printing technology have made it possible
to fabricate metamaterials with characteristic mechanical properties, it is not
easy to fabricate complex shapes containing cavities. In this study, a
composite structure comprising two types of materials without a cavity was
optimized. Moreover, a mechanical metamaterial with a negative Poisson's ratio
that can be fabricated using an additive manufacturing method was developed.
First, a homogenization method that characterizes the properties of composite
structures was briefly described. Then, an optimization problem to realize a
negative Poisson's ratio was formulated, and a level set-based topology
optimization method was proposed to solve the abovementioned problem. Next,
three-dimensional numerical examples are presented to confirm the effectiveness
of the proposed method, and the deformation behaviors of the optimized designs
are numerically examined. Furthermore, a sample containing the optimized design
with negative Poisson's ratio for the tensile test was fabricated using a 3D
printer. We conducted some experiments to evaluate its mechanical performance.
