ABSTRACT
A material is deŸned to be elastic if it deforms when a force is applied to it, but returns to its original conŸguration without energy dissipation when the applied force is removed. Consider the uniform thin cylindrical wire shown in Figure 2.1a with an undeformed length ℓ0 subjected to a normal tensile load P. The wire will elongate by a magnitude δ due to the axial load. The average normal stress that the wire is subjected to can be computed as σ = P/A, where A is the cross-sectional area of the wire in the undeformed conŸguration. The normal stress has the units of force per unit area. In the SI system, stress has the dimensions of N/m2 and is referred to as pascal (Pa). The magnitudes for stress occurring in engineering practice are relatively large and hence preŸxes such as kPa (kilopascal = 103 Pa), MPa (megapascal = 106 Pa), or GPa (gigapascal = 109 Pa) are usually employed. When the wire is stretched in the axial direction, there will be a reduction in the cross-sectional area. This fact can be demonstrated easily by stretching an elastic band and it can be observed that the cross-sectional area decreases with increase in axial stretch. The decrease in dimensions is not large enough to be observed by visual inspection in most engineering materials. In usual engineering practice, the stress is deŸned based on the cross-sectional area of the undeformed conŸguration rather than the instantaneous value and the error introduced will be negligible.
