The linear elastic behaviour corresponds to a material working in the first part of the curve, in the range of the small deformations. Under these conditions, the material behaviour is described by elastic modulus E, where E is the initial slope of the stress - strain curve, therefore the proportionality is constant between stresses and strains in the material.
A second parameter (Poisson's ratio) is introduced in order to define the relationship between the transversal and longitudinal strains measured in the material. In the case of a homogeneous and isotropic material, these 2 values are enough for the full description of the linear elastic behaviour.
When plastic deformations are not present, the processes of loading and unloading of a linear elastic material follow the same pattern. This process is conservative, energy dissipation does not exist.
Linear elastic behaviour could be represented by a simple mechanical model, a linear spring with stiffness E. When a load of magnitude σ is applied to the spring, a deformation ε is obtained, with the condition that it will return to the initial position when the spring is unloaded, throughout a process without energy dissipation.