Hooke (1676), Young (1807), Cauchy (1822) and Timoshenko (1934) have said almost everything about the linear-elastic behaviour of materials. In this field, we will therefore limit ourselves to giving a summary in the form of formulae. However, we will deal with anisotropic elasticity, which is so important for composite materials, and the identification of the coefficients. The term elasticity is taken here to mean the reversible deformations mentioned in Chapter 3. Neither thermal dissipation (thermoelasticity) nor mechanical dissipation (viscoelasticity) is excluded.

Thermoelasticity introduces several additional coefficients into the constitutive law including the dilatation coefficient, and permits the treatment of problems involving temperature variations, such as thermal stress analysis problems.

The theory of viscoelasticity was developed considerably with rheology during the 1960s. We will restrict ourselves in this chapter to linear viscoelasticity which is sufficient to deal with the mechanical behaviour of certain polymers.

These theories are continuum theories; the inhomogeneities are assumed to be small enough with respect to the size of the volume element that the results of experiments conducted on the latter are really the characteristics of average macroscopic behaviour. This is also true for composite materials and concrete whose behaviour can be more accurately described by homogenization techniques.

Elasticity

Domain of validity and use

All solid materials possess a domain in the stress space within which a load variation results only in a variation of elastic strains.