Abstract-Foams have previously been fabricated with a negative Poisson's ratio (termed auxetic foams).A novel model is proposed to explain this and to describe the strain-dependent Poisson's function behaviour of honeycomb and foam materials. The model is two-dimensional and is based upon the observation of broken cell ribs in foams processed via the compression and heating technique usually employed to convert conventional foams to auxetic behaviour. The model has two forms: the "intact" form is a network of ribs with biaxial symmetry, and the "auxetic" form is a similar network but with a proportion of cell ribs removed. The model output is compared with that of an existing two-dimensional model and experimental data, and is found to be superior in predicting the Poisson's function and marginally better at predicting the stress-strain behaviour of the experimental data than the existing model, using realistic values for geometric parameters.

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ABSTRACT--The Poisson's ratio of a material is strictly defined only for small strain linear elastic behavior. In practice, engineering strains are often used to calculate Poisson's ratio in place of the mathematically correct true strains with only very small differences resulting in the case of many engineering materials. The engineering strain definition is often used even in the inelastic region, for example, in metals during plastic yielding. However, for highly nonlinear elastic materials, such as many biomaterials, smart materials and microstructured materials, this convenient extension may be misleading, and it becomes advantageous to define a strainvarying Poisson's function. This is analogous to the use of a tangent modulus for stiffness. An important recent application of such a Poisson's function is that of auxetic materials that demonstrate a negative Poisson's ratio and are often highly strain dependent. In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated. Interpretation methods for coping with error-sensitive data or small strains are also described.KEY WORDS--Engineering strain, nonlinear, Poisson's ratio, strain dependent, true strain, auxetic Nomenclature e = engineering strain (also known as nominal or Cauchy) Io = starting length li = length s = true strain (also known as Hencky strain) s int : instantaneous true strain s l~ = log transform true strain S t~ ~-total instantaneous true strain v = Poisson's ratio or function i) eng = Poisson's ratio (engineering strain) 1) int :Poisson's ratio (instantaneous true strain) 1) l~ = Poisson's ratio (log transform true strain) )3 t~ = Poisson's function (total instantaneous true strain)

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