9.1 Introduction

Let us consider the geometrical change in time (the deformation and movement in three-dimensional space) of a coherent amount of material or material fraction, for which a continuum modelling approach is allowed. In case more fractions are involved, it is in principle possible to describe the behaviour of each fraction separately, as if it was isolated from the other fractions (however it wil be necessary to include interactions between fractions). The present chapter is focussed on a detailed description of motion. In addition, the consequences of configuration changes for the formulation of physical fields will be discussed. There will be no attention to the possible causes of the motion. In the present chapter, an approach will be followed that is common practice in the continuum description of solids (although it can also be applied to fluids). The specific aspects relevant for fluids will be treated at the end of the chapter.

9.2 Geometrical Description of the Material Configuration

Consider a coherent amount of material in a completely defined geometrical state (the reference configuration). From each material point P, that can be allocated, the position vector (with components stored in the column ) is known. In the following, this position vector will be used to identify the material point. The vector is inextricably bound to the material point P, as if it were an attached label. With respect to a Cartesian xyz-coordinate system, can be written as

Because is uniquely coupled to a material...