The mechanics of rubber elasticity

Abstract

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 I 1 and I 2 . The experiments of Rivlin & Saunders indicated that ∂ W /∂ I 1 was approximately constant while ∂ W /∂ I 2 varied with I 2 , in contrast to the Mooney equation, according to which both ∂ W /∂ I 1 and ∂ W /∂ I 2 are constant. More recently it has been proposed by Valanis & Landel that W may be expressible in terms of separate functions w ( λ i ) of the principal extension ratios λ i 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 ( λ i ) to be expressed as an explicit algebraic function, from which it appears that the earlier conclusions of Rivlin & Saunders require some modification in detail.