Static indifferent states

If we express the state of a system in terms of intensive variables, then the representative points of a system in equilibrium form a continuum in w dimensions. The equilibrium indifferent states, or static indifferent states, will also be represented in this continuum but they must satisfy in addition, the further ( - 1) conditions of indifference (29.19). These ( - 1) relations among the w variables leave only one independent variable the static indifferent states of the system hence fall on a line, called the indifferent line. 

We met these theorems in studying the properties of states of uniform composition (chap. XVIII, 6) we shall now examine them in a more general form as a property of all static indifferent states in a poly variant system. 

Let us suppose that we are given the initial masses at random, and let us enquire whether the closed system thus constituted can exist in an indifferent state, whether static or not. This clearly cannot be possible unless there exists an indifferent state in which the weight fractions satisfy the 1-f-c - (0-f-/) conditions of compatibility. However, the composition variables must also satisfy the 1- (r + r") equations A. In all we have therefore... 

Indeed, carbon black-filled rubber, when loaded with time-dependent external forces, suffers a state of stress which is the superposition of two different aspects a time independent, long-term, behavior (sometimes improperly called hyperelastic ) opposed to a time dependent, short-term, response. Step-strain relaxation tests suggest that short term stresses are larger than the long term or quasi-static ones [117]. Moreover, oscillatoiy (sinusoidal) tests indicate that dissipative anelastic effects are significant, which leads to the consideration of a constitutive relation which depends not only on the current value of the strain but on the entire strain history. This assumption must be in accordance with some principles which restrict the class of rehable constitutive equations. These restrictions can be classified as physical and constitutive . The former are restrictirMis to which every rational physical theory must be subjected to, e.g., frame indifference. The latter, on the other hand, depends upon the material under consideration, e.g., internal symmetries. 

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