Motivation

Material behaviour at length scales greatly in excess of molecular dimensions (i.e., macroscopic behaviour) is usually modelled in terms of the continuum viewpoint. From such a perspective the matter associated with any physical system (or body) of interest is, at any instant, considered to be distributed continuously throughout some spatial region (deemed to be the region ‘occupied’ by the system at this instant). Reproducible macroscopic phenomena are modelled in terms of deterministic continuum theories. Such theories have been highly successful, particularly in engineering contexts, and include those of elasticity, fluid dynamics, and plasticity. The totality of such theories constitutes (deterministic) continuum mechanics. The link between actual material behaviour and relevant theory is provided by experimentation/observation. Specifically, it is necessary to relate local experimental measurements to continuum field values. However, the value of any local measurement made upon a physical system is the consequence of a local (both in space and time) interaction with this system. Further, local measurement values exhibit erratic features if the scale (in space-time) is sufficiently fine, and such features become increasingly evident with diminishing scale. Said differently, sufficiently sensitive instruments always yield measurement values which fluctuate chaotically in both space and time (i.e., these values change perceptibly, in random fashion, with both location and time), and the ‘strength’ of these fluctuations increases with instrument sensitivity (i.e., with increasingly fine-scale interaction between instrument and system).