Shape memory and phase transitions for auxetic materials

Abstract

We present a mathematical model describing the auxetic-austenitic phase transition phenomenon by a second order shape memory phase transition. The typical properties of auxetic materials, as the negative Poisson ratio ν, are described by a function of the phase ϕ, called order parameter, which relates the phase transition with a change of the internal order structure of the material. In our model, the auxetic phase is represented by an order parameter ϕ = 1, which provides a negative Poisson's ratio, while the austenitic phase will be denoted by ϕ = 0

Auxetic deformation of the weft-knitted Miura-ori fold

“…Mechanical analysis and modeling of auxetic response help to reveal the NPR effect for further expansion of its applications. Until now there have been many algorithms that have been employed to study the deformation mechanism of auxetic materials, including firstprinciple, 23,24 continuum mechanics, 25 finite element analysis (FEA), 26 the differential method 27 and other mathematical methods. Among them, FEA models provide possibilities to simulate mechanical behaviors of NPR materials in the macro-scale.…”