Strain-Gradient Modeling and Computation of 3-D Printed Metamaterials for Verifying Constitutive Parameters Determined by Asymptotic Homogenization

Metamaterials exhibit significantly different mechanical deformation than in classical “first-order” theory. One possible modeling approach is to use a “straingradient” theory by incorporating also higher gradients of displacements into the formulation. This procedure clearly brings in additional constitutive parameters. In this study, a numerical framework is presented by applying strain-gradient theory to 3-D printed structures with an infill ratio used frequently in additive manufacturing for weight reduction. This choice causes metamaterials; the additional constitutive parameters in the strain-gradient model are determined by an asymptotic homogenization. In order to demonstrate the reliability of this methodology, we verify the accuracy by computations using the finite element method.