An Energy Balance for Deformation and Fracture

The quantity SUi represents that energy dissipated by plastic or viscous flow being converted to heat. Two subcases must be considered—adiabatic systems 

Introduction to Physical Polymer Science, by L.H. Sperling ISBN 0-471-70606-X Copyright 2006 by John Wiley Sons, Inc. 

The quantity 5Uj, indicates the stored elastic energy in the system (note the springs in Chapter 10) but also includes stored thermal energy. The quantity 5U indicates changes in energy associated with changes in linear or angular velocity. 

For the isothermal case where the stored energy is solely elastic, the net input of energy can be written 

Now consider that the body undergoes a displacement du. Then 

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