Rubber Stretched by Forces in Two Directions Perpendicular to One Another

Abstract

Abstract In previous publications the author has defined by means of relatively simple expressions, the behavior of rubber under tension and under compression. However, as was mentioned in a book entitled “Finite deformations” by the author, it is not possible to develop a theory of elasticity for highly deformable objects, which have their prototype in rubber, unless it is known how they behave when each element is acted upon by the primary three forces which, according to the theory of finite deformations, as well as the ordinary theory of elasticity or again the theory of infinitesimal deformations, are sufficient to define each state of tension. With regard to the last theory, the linear relation between deformation and stress makes it possible to accept the principle of the superposition of simultaneous forces, i. e., to add algebraically all coexistent forces and deforma- tions. However, this is obviously impossible for finite deformations, for which the linear relation in question has not been confirmed. Rather than proceed on the basis of hypotheses to develop theories and to verify them by deductions, it seemed more reasonable to undertake an experimental investigation, which later would serve as a background for the theoretical development of the problem. As a beginning, the case of the coexistence of two principal stresses in a relatively thin film has been considered. The experimental results are described in the present paper and will be discussed in a forthcoming paper.