27.2 : 应变能密度

An axial load causes a rod to elongate, and store strain energy in it. The strain energy density in the rod is the energy per unit volume.

Here, the ratio of the axial force to the area is stress, and the ratio of elongation to the original length of the rod is the strain produced.

Within the elastic region, the strain energy density can be expressed in terms of the modulus of elasticity.

The stress-strain curve exhibits a linear relationship in the elastic region, implying that the strain energy density follows Hooke's Law. Here, upon removing the stress, the strain becomes zero. This region of energy density is called the modulus of resilience.

In the plastic region, some permanent strain remains even after removing the stress. So, only part of the strain energy density is recovered, and the remaining energy density is spent in deforming the object in the form of heat. 

The total area under the curve is called the modulus of toughness and represents the total energy density required to rupture the rod.