Vectors and Cartesian Tensors

Abstract

The mathematical concepts associated with the study of solid mechanics, like those of elementary mechanics, may be represented using nothing more than ordinary scalar and vector mathematics. The use of such mathematics has, however, generally been found to be somewhat awkward and lengthy and it has become popular in recent years to employ instead the unified mathematics of tensors—and, in particular, Cartesian tensors — for representing these concepts in a clearer and more concise fashion. In keeping with this modern trend, Cartesian tensors will therefore be employed throughout this book. We accordingly begin our study of solid mechanics with a brief review of certain ideas from vector analysis as expressed in the tensor notation and subsequently use these ideas to introduce the more general concept of Cartesian tensors.