Entropy Effects and Rubber Elasticity

A tensile force applied to a linear elastic bar does a certain amount of work as the bar is stretched defined by the relation. 

One method to approximate adiabatic testing is to perform the test rapidly enough that no heat is lost from the sample but not so rapid that dynamic or inertia effects occur. Mueller (1969) gives experimental results obtained by cyclic testing 2.5 cm diameter steel bars in tension, compression and torsion with a loading-unloading cycle of about one minute in duration. In a tensile test he shows a decrease in temperature of approxi- 

Lubliner (1990), and other texts for a more thorough treatment of the mathematics of the thermodynamic effects related to either reversible of irreversible processes of deformed solids. 

The relationship between energy, entropy and temperature for reversible processes is best described using the first and second law of thermodynamics. The first law relates the change in internal mechanical energy, dU, and the change in internal thermal energy (heat), dQ, to the work done on the system by external forces, dW, and is given as. 

The second law of thermodynamics defines the entropy change, dS, in a reversible process such that, 

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