Optimizing the auxetic behavior of anisotropic laminates

TL;DR

This paper investigates how to optimize the auxetic properties of orthotropic laminates, focusing on maximizing negative Poisson's ratio and auxetic zones using boundary solutions and angle-ply sequences.

Contribution

It introduces a boundary-based optimization approach for auxeticity in laminates using polar methods and dimensionless invariants for anisotropic behavior.

Findings

Optimal solutions are on the boundary of the feasible domain.

Angle-ply sequences of identical layers achieve optimal auxetic properties.

The polar method simplifies the representation of anisotropic behavior.

Abstract

Anisotropic laminates with a negative Poisson's ratio for at least some directions are called auxetic. In this paper, we consider the conditions for optimizing the auxeticity of an orthotropic laminate, namely: for a laminate composed by a given material, (i) how to obtain the lowest, i.e. the highest negative, Poisson's ratio and (ii) how to maximize the auxetic zone, i.e. the set of directions where the Poisson's ratio is negative. It is shown that in both the cases the optimal solution is found on the boundary of the feasible domain and in particular that it can be obtained using angle-ply sequences of identical layers. The polar method with dimensionless moduli is employed for representing the anisotropic behavior of the laminate, which allows, on the one hand, to reduce the dimensionality of the problem and, on the other hand, to have an effective mathematical representation of anisotropy by dimensionless invariants.