INTRODUCTION TO TENSOR CALCULUS

Abstract

In the first part we have considered one-dimensional models to describe material behavior. The application of such models, however, is rather limited, since in the general case, both the stress and the strain state are three-dimensional. For the generalization of such concepts to higher dimensions than one, an appropriate mathematical instrumentarium is needed. In mechanics, the appropriate objects for the mathematical description are vectors and tensors. For readers not familiar with such objects, we will next give a brief introduction into tensor algebra and analysis.