Abstract
Common observations indicate that material bodies undergo motion and deformation as a result of applied forces. In this chapter, we will be concerned with the development of quantitative measures of these kinematical variables based on the continuum hypothesis. Included in this effort is the description of motion and displacement, and this will lead to the construction of several strain tensor measures. Since we wish to formulate time-dependent behaviors, various dynamic variables and rate of strain tensors will also be developed. Results in this chapter by themselves will not yet be able to predict the deformation resulting from the applied loading. Other relations will need to be constructed and combined with the work here to develop a complete mechanistic theory.
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