Integrated shape and size optimization of curved tetra-chiral and anti-tetra-chiral auxetics using isogeometric analysis

Abstract

Taking advantage of the powerful design potentials of isogeometric analysis, an integrated shape and size optimization framework for designing tetra chiral and anti-chiral auxetics is proposed to be capable of obtaining excellent designs without complicated implementation efforts. The framework utilizes a non-uniform rational basis spline (NURBS) based parametrization method that describes the chiral and anti-chiral structures with a small number of size and shape parameters. With this effective framework, systematic design studies considering both plane strain and stress conditions are performed to provide bounding graphs for the best achievable auxeticities under different stiffness requirements. Designs with tunable effective properties are also provided to demonstrate the capabilities of the proposed framework. The potential for electronic-skin applications is illustrated.