Preamble

Continuum mechanics is the study of material behaviour as manifest at macroscopic scales of length and time. Irrespective of molecular constitution, or whether the material is gaseous, liquid, or solid, mathematical descriptions of such behaviour have a common foundation. This foundation has been developed in Chapters 3 through 8, and is codified in terms of the system of balance relations for mass, linear and rotational momentum, and energy, and the physical descriptors (i.e., fields) which appear therein. Such relations, which serve as evolution equations for mass etc., involve terms directly related to molecular behaviour, but take the same form regardless of the specific and explicit scales of length and time associated with the averaging procedure.

In order to model a particular material system, with the aim of predicting its behaviour under prescribed circumstances, it is necessary

1. (i) to distinguish this behaviour from that of other materials subjected to the same prescribed circumstances, and

2. (ii) to make precise just what is intended by ‘prescribed circumstances’.

In respect of prescription (i), the nature (or ‘constitution’) of an individual system is identified in terms of constitutive relations which specify the ‘response’ of the material to the consequences of prescribed circumstances. Prescription (ii) involves specification of agencies external to the system (including the effect of gravity and of contact between the system and the exterior world across its boundary) together with initial information.