The determination of the equivalent strain in finite, homogeneous deformation processes

Abstract

This article considers the in-plane deformation of a thin, incompressible membrane undergoing an arbitrary, but finite, homogeneous deformation mode. No discontinuities in the loading system are permitted, and the nature of the straining process is assumed unchanged from beginning to end. For these restricted deformation modes a technique is described whereby the equivalent strain can be evaluated by measuring the initial and final shape only of a finitely deformed grid marked on the surface of the membrane. The analysis is performed with reference to an initially square or rectangular grid of lines, since the nodes of the grid facilitate the experimental measurements. A distinction is drawn between homogeneous deformation and the special case of pure homogeneous deformation which results in the same shape change. In the latter mode a pair of principal axes can be identified which remain orthogonal during the entire deformation history; while for the former mode there is no such line pair which preserves orthogonality throughout the deformation. The article concludes with a brief discussion on the determination of strain in industrial stampings.