Mechanics of Solids, 2nd Edition

CHAPTER 11

Strain Energy

11.1 Strain Energy due to Normal Stresses

The idea of strain energy was introduced in Chapter 4. The strain energy density, also called strain energy intensity was defined as strain energy stored in a body per unit of its volume. Consider a small element of edges d_x, d_y and d_z and normal stress σ_xx is acting along x-axis. (see Fig. 11.1). The force due to σ_xx acting on the area d_y d_z is σ_xx d_y d_z. If the strain along x is ε_xx, the force σ_xx d_y d_z has moved through a distance which is equal to increase in size d_x. This increase is ε_xx d_x. Hence the work done by the force

 

 

 

Fig. 11.1

 

Apparently the stress