Systematic design of tetra-petals auxetic structures with stiffness constraint

Abstract

This paper focuses on a systematic isogeometric design approach for the optimal petal form and size characterization of tetra-petals auxetics, considering both plane stress and plane strain conditions. The underlying deformation mechanism of a tetra-petals auxetic is analyzed numerically with respect to several key parameters. Design optimizations are performed systematically to give bounding graphs for the minimum Poisson's ratio achievable with different stiffness constraints. Tunable design studies with targeted effective Poisson's ratio, shear modulus and stiffness are demonstrated. Potential application for functionally graded lattice structures is presented. Numerical and experimental verifications are provided to verify the designs. The out-of-plane buckling phenomenon in tension for thin auxetics with re-entrant features is illustrated experimentally to draw caution to results obtained using plane stress formulations for designing such structures.