A geometric determination of void production in an elastic pancake

摘要

AbstractThe 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,veff, which is consistent with the measured values of γ = −u0(a)/aε (normalized volumetric contraction), the initial modulus from the triaxial tests on compression,Mcompr, and tension,Mtens. In order to obtain analytical expressions relating γ and (M/E)tenstoveff, we used the simplest finite element mesh. Taking the given aspect ratio of the pancakedocumentclass{article}pagestyle{empty}begin{document}$$ left( {frac{{rm D}}{{rm h}} approx 16} right) $$end{document}, the shear modulusG= 60 psi, and the measured γ = 0.23, it was found that the effective Poisson's ratio isveff≈ 0.492 and the initial modulus in tensionMtens= 2990 psi. Using Warren's equation, one obtains the volume fraction of voids from the determined effective material propertyveff. It was found that the volume fraction of voids α grows from 0.002 to 0.021. © 1993 John Wiley