ABSTRACT
Rheology is a term formally introduced by Bingham in 1929 to designate the
study of deformation and flow of matter [1]. It is evident from daily experi-
ence that materials can flow or deform under the action of body forces, i.e.,
their own weight or surface forces, applied over their boundaries (solid
contours, free surface), and behave quite differently, both qualitatively and
quantitatively. Indeed, the original definition of rheology seems to open a
very large horizon spacing from highly rigid solids to low-density fluids.
More precisely, the borders of this relatively young science are more
restricted and marked by other more mature disciplines, belonging to the
continuum mechanics family, such as the elasticity theory and the Newtonian
fluid mechanics, which are more suitable to describe simple mechanical
behaviors. In both cases only a physical property (elastic modulus or viscos-
ity) is sufficient to describe the deformation or flow conditions produced by
the stresses acting on the material. Just for their si mplicity such approaches
hold only for a limited class of materials and under limiting conditions of flow
and deformation. Many real substances exhibit more complex behaviors,
which can be accommodated between the two extremes settled by the linear
models proposed by Hooke and Newton. This is the reason why rheology
emerged in the past twenties as an independent science to describe phenom-
ena and to solve problems inaccessible by the classical approaches. In other
words, the specific objective of rheology is the definition of constitutive
equations or models suitable to account for the stress-strain relationships
observed for real systems. Such equations, combined with the principles of
continuum mechanics, can then be used positively in the resolution of flow and
deformation problems which cannot be tackled with the classical approaches. In
this sense rheology represents a natural expansion and a necessary integration
of the continuum mechanics.
