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The strain energy will in general vary throughout a body and for this reason it is useful to introduce the concept of strain energy density, which is a measure of how much energy is stored in small volume elements throughout a material.
Strain energy density is the amount of strain energy absorbed per unit volume of the object. It is also known as the amount of work required to cause deformation in a unit volume of the object. It is denoted by the symbol ‘u’ and it is equal to the area under the stress-strain curve.
We prefer to normalize strain energy by unit volume, and when we do so, this is referred to as strain energy density. The area under a stress-strain curve is the energy per unit volume (stress*strain has units of force per area such as N/mm2, which is the same as energy per unit volume N-mm/mm3. We will be assuming linear elastic material only.
Strain energy density (g se /(kJ/m 3)), which is defined as the energy dissipated per unit volume during the strain-hardening process, is equal to the area enclosed by the ascending branch of the stress-strain curve (see Fig. 3.19 a) and can be calculated by Eq.
The units of energy are force*distance, so when a load is applied and the material deforms, we are putting energy into the material. This energy is referred to as “strain energy.”. We prefer to normalize strain energy by unit volume, and when we do so, this is referred to as strain energy density.
Define the stress-strain relation for the solid by specifying its strain energy density W as a function of deformation gradient tensor: W=W(F). This ensures that the material is perfectly elastic, and also means that we only need to work with a scalar function.
Figure 3.1: Stress-strain curve for a linear elastic material subject to uni-axial stress ˙(Note that this is not uni-axial strain due to Poisson e ect) In this expression, Eis Young’s modulus. Strain Energy Density For a given value of the strain , the strain energy density (per unit volume) = ^( ), is de ned as the area under the curve.
