Date of Award


Document Type



Santa Clara : Santa Clara University, 2019.

Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Michael Taylor


In this investigation, the main interest was studying low porosity auxetic metamaterials generated out of linearly elastic materials, meaning bodies made out of linearly elastic materials (e.g., metals) that, due to alternating patterns of elongated voids perforated on them, exhibit a negative effective Poisson ratio (property commonly called auxeticity). This kind of metamaterials, often obtained by a pattern of elongated ellipsis, generally face the issue of presenting high stress concentration when loaded. The objective of this study is to solve this problem by adding rounded shapes (stop-holes) at the end of elongated grooves, as a replacement for the previously mentioned elongated elliptical voids. Particularly, the “superformula”, a generalized ellipse equation in polar coordinates, was utilized in this investigation as a way of parametrization to determine the shapes to be added in a flexible through way by the alteration of 6 parameters. For the process of choosing adequate parameters to ensure optimum stress concentration, firstly, a careful selection from a catalog of shapes took place. Then, static FEA simulations of a totally parametric Representative Volume Element model that included the selected shapes were executed. To do this computer scripts were developed for interconnecting the operation of multiple engineering software tools. Finally, the effect that the size of the stop-holes, thus the porosity, had over the stress induced in the material and its auxetic deformation response due to the new geometry of the pattern of voids was evaluated. The investigation successfully found shapes that produced a significant stress reduction, by reducing the stress concentration, and in the process found several corollaries and observations of the behavior of the metamaterial depending on the shape and size of the stop-holes.