Next, we will comment on the models of real behaviour, starting with the simplest:
Rheology studies the relationship between the stress tensor, strain tensor and speeds.
The linear elastic behaviour relates to a material working at the beginning of the curve, in the range of small deformations. Under these conditions, the behaviour of the material is described by elastic modulus E. E is the initial slope of the stress - strain curve, so that the proportionality is kept constant between stresses and strains in the material.
A second parameter (Poisson's ratio) is introduced in order to define the relation between the transverse and longitudinal strains measured in the material. In the case of homogeneous and isotropic materials, these two values are enough to get the full description of linear elastic behaviour.
When plastic deformations are not present, the processes of loading and unloading a linear elastic material follow the same behaviour. This process is conservative, meaning that energy dissipation does not occur.
Linear elastic behaviour could be represented by a simple mechanical model, a linear spring with stiffness E. If a load of magnitude σ is applied to the spring, a deformation ε is obtained, with the condition of return to the initial position in case of spring unloading, throughout a process without energy dissipation.