Metal behavior laws - Elasticity. Viscoelasticity

Elastic behavior is characterized by the fact that, after unloading the structure, no residual deformation remains. The behavior is perfectly reversible. The state of deformation is independent of the loading path, and there is an elastic potential.

The stress and strain tensors are linked by a bijective relationship. The work involved in moving from one equilibrium state to another can be considered the elastic potential.

For many materials, there is a domain where elastic behavior is linear, i.e. deformations are proportional to stresses. Such behavior is the most familiar, the best known and the most widely used in structural design.

In elasticity, time does not intervene. However, viscous behavior is characterized by the intervention of time. A viscoelastic material therefore has a behavioral law that is reversible, but in which time is involved. After discharge, no residual deformation remains, but under constant load, deformation evolves; at constant deformation, stress varies; more generally, stress depends on the rate of deformation, its acceleration, and possibly higher-order time derivatives.

A linear relationship between stress and strain and their successive derivatives with respect to time corresponds to linear viscoelastic behavior. But many materials do not obey such a law, and are non-linear viscoelastic.

The following chapter is devoted successively to these two types of behavior, first elastic, then viscoelastic. It describes the corresponding behavior laws and how to determine their coefficients using mechanical tests.