A geometric determination of void production in an elastic pancake

The aim of this article is to adduce various theoretical approaches to evaluating the stress displacement field throughout a pancake sample. We shall attempt to produce an effective material property, v_eff, which is consistent with the measured values of γ = −u₀(a)/aε (normalized volumetric contraction), the initial modulus from the triaxial tests on compression, M_compr, and tension, M_tens. In order to obtain analytical expressions relating γ and (M/E)_tens to v_eff, we used the simplest finite element mesh. Taking the given aspect ratio of the pancake \documentclass{article}\pagestyle{empty}$$ \left( {\frac{{\rm D}}{{\rm h}} \approx 16} \right) $$ , the shear modulus G = 60 psi, and the measured γ = 0.23, it was found that the effective Poisson's ratio is v_eff ≈ 0.492 and the initial modulus in tension M_tens = 2990 psi. Using Warren's equation, one obtains the volume fraction of voids from the determined effective material property v_eff. It was found that the volume fraction of voids α grows from 0.002 to 0.021. © 1993 John Wiley & Sons, Inc.