Tensors

Abstract

As seen previously in the introductory chapter, the goal of continuum mechanics is to establish a set of equations that governs a physical problem from a macroscopic perspective. The physical variables featuring in a problem are represented by tensor fields, in other words, physical phenomena can be shown mathematically by means of tensors whereas tensor fields indicate how tensor values vary in space and time. In these equations one main condition for these physical quantities is they must be independent of the reference system, i.e. they must be the same for different observers. However, for matters of convenience, when solving problems, we need to express the tensor in a given coordinate system, hence we have the concept of tensor components, but while tensors are independent of the coordinate system, their components are not and change as the system change.