## ABSTRACT

In the application of forces or displacements to a body, the effects are observed by the measurement of displacements (or strains). To predict the behaviour, tests must be carried out on specimens of the material to determine not only the elastic constants of the material but also the laws for its behaviour in the inelastic range. The determination of material properties can be an exacting task, particularly if they are required over the whole range of temperatures up to the softening point of the material. Such information is, of course, vitally necessary in thermal stress analysis, e.g. in the calculation of residual welding stresses where extremely high temperatures occur. Since all problems in the inelastic range may be treated as being composed of linear steps, it is essential first to study elastic (or linear) behaviour. Linear elastic behaviour is characterized by a linear relationship between forces and the corresponding displacements. This study leads to the definitions of strain and stress and the relationships (or constitutive laws), between these two quantities. Strain is the more natural phenomenon to study first because it is the observed quantity. With this in mind the concepts of strain will be introduced, followed by those of stress and the constitutive relationships which connect the two. In keeping with the spirit of the text the theory is presented in index notation, but where results are also useful in matrix form from the viewpoint of computational mechanics, both will be given.