## Ideal Elastic Solids

An ideal elastic solid is often referred to as a Hookean solid, after Robert Hooke, the scientist who first described this type of behavior (Whorlow 1992, Macosko 1994, Rao et al. 1995). Hooke observed experimentally that there is a linear relationship between the deformation of a solid material and the magnitude of the force applied to it, provided the deformation is not too large (Figure 8.1). He also observed that when the force was removed from the material, it returned back to its original length. In general, Hooke found that the force per unit area (or stress) was proportional to the relative deformation (or strain). Hooke's law can therefore be summarized by the following statement:

A stress can be applied to a material in a number of different ways, including simple shear, simple compression, and bulk compression (Figure 8.2). Equation 8.1 is applicable to each of these situations, but the values of the stress, strain, and constant used depend on the nature of the deformation (Table 8.1).

The equations given in Table 8.1 assume that the material is homogeneous and isotropic (i.e., its properties are the same in all directions). To characterize the rheological constants of an ideal elastic solid, it is therefore necessary to measure the change in its dimensions when a force of known magnitude is applied.

The elastic behavior of a solid is related to the intermolecular forces which hold the molecules together. When a stress is applied to a material, the bonds between the molecules are compressed or expanded, and therefore they store energy. When the stress is removed, the bonds give up this energy and the material returns to its original shape. The elastic modulus

Breaking Point i

Breaking Point

Strain

FIGURE 8.1 At small deformations, there is a linear relationship between the applied stress and the resultant strain for an ideal elastic solid. At higher deformations, the stress is no longer linearly related to strain and the material will eventually break.

### Strain

FIGURE 8.1 At small deformations, there is a linear relationship between the applied stress and the resultant strain for an ideal elastic solid. At higher deformations, the stress is no longer linearly related to strain and the material will eventually break.