Poisson distribution

Statistics

Physics

Engineering

Mathematical analysis

Finite element method

Poisson's ratio

Composite material

Boundary value problem

Materials science

Modulus

Young's modulus

Geometry

Mathematics

Mechanics

Boundary (topology)

Auxetics

Structural engineering

Composite Structures

This paper presents an analytical framework with a bottom-up multi-step approach to predict the in-plane mechanical properties including the effective Young’s modulus and Poisson’s ratio in two directions. There are deviations for the analytical predictions with respect to the numerical results because of the simplifications of boundary conditions of the representative unit cell. To remedy the deviations, a modification coefficient is embedded to revise the analytical model. A finite element code for obtaining elastic properties of the irregular auxetic structures is developed to validate the revised analytical model. The good agreement between the revised analytical predictions and numerical results affirms the accuracy of the revised analytical model. It is noticeable that the effects of irregularity on the effective Young’s modulus are more prominent than on the Poisson’s ratio.

Effective elastic properties of irregular auxetic structures