The mechanics of rubber elasticity

The mechanical properties of a rubber may conveniently be represented in terms of the strain energy W, which in Rivlin’s notation is expressed as a function of the strain invariants I1 and I2. The experiments of Rivlin & Saunders indicated that ∂W/∂I1 was approximately constant while ∂W/∂I2 varied with I2, in contrast to the Mooney equation, according to which both ∂W/∂I1 and ∂W/∂I2 are constant. More recently it has been proposed by Valanis & Landel that W may be expressible in terms of separate functions w(λi) of the principal extension ratios λi This hypo­ thesis appears to be borne out experimentally, and gives promise of a more accurate analysis of experimental measurements. Application to recent data enables w(λi) to be expressed as an explicit algebraic function, from which it appears that the earlier conclusions of Rivlin & Saunders require some modification in detail.