  This paper aims to understand the role of directional material properties on
the mechanical responses of origami structures. We consider the Miura-Ori
structures our target model due to their collapsibility and negative Poisson's
ratio (NPR) effects, which are widely used in shock absorbers, disaster
shelters, aerospace applications, etc. Traditional Miura-Ori structures are
made of isotropic materials (Aluminum, Acrylic), whose mechanical properties
like stiffness and NPR are well understood. However, how these responses are
affected by directional materials, like Carbon Fiber Reinforced Polymer (CFRP)
composites, lacks in-depth understanding. To that end, we study how fiber
directions and arrangements in CFRP composites and Miura-Ori's geometric
parameters control the stiffness and NPR of such structures. Through finite
element analysis, we show that Miura-Ori structures made of CFRP composites can
achieve higher stiffness and Poisson's ratio values than those made of an
isotropic material like Aluminum. Then through regression analysis, we
establish the relationship between different geometric parameters and the
corresponding mechanical responses, which is further utilized to discover the
Miura-Ori structure's optimal shape. We also show that the shear modulus is a
dominant parameter that controls the mechanical responses mentioned above among
the individual composite material properties within the Miura-Ori structure. We
demonstrate that we can optimize the Miura-Ori structure by finding geometric
and material parameters that result in combined stiffest and most compressible
structures. We anticipate our research to be a starting point for designing and
optimizing more sophisticated origami structures with composite materials
incorporated.
