Abstract
The under-determined equation M(F,D,dF/dt,dD/dt)=0, where F=F(t), D=D(t) are measures of force and deformation and t is time, can be transformed into a first-order partial differential equation in F, D, ∂F/∂D, ∂F/∂t whose characteristics represent the totality of all possible force-elongation trajectories in F, D, t space. Historically, M has seen considerable service either as a complete stress-strain relation or an element in a distribution of such relations. A geometric interpretation of M useful in rheological studies of fibers is given. Necessary conditions are given for M to provide a satisfactory description of a fiber's mechanical behavior. An operational procedure is outlined for constructing M in the laboratory based on direct measurements instead of on a priori assumptions involving springs and dash pots. The discussion is brief and theoretical.
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