What Is Strain Energy?
The potential energy stored in an object in the form of strain and stress is also called deformation energy.
The potential energy stored in an object in the form of strain and stress is also called deformation energy.
- Chinese name
- Strain energy
- Foreign name
- strain energy
Strain energy text
Taking a one-dimensional problem as an example, a straight rod of constant cross section with a cross-sectional area of A and a length of L is elongated by the external axial force P1. (figure 1). If the dynamic effect and temperature effect during the deformation process are not taken into account, all the work W performed by the external force is stored in the rod, and it becomes the strain energy U of the rod, and its value is:
Where P is the elongation during deformation Corresponding load. P- shown in Figure 2 In the curve, the area under the curve is equivalent to the strain energy in the rod. Corresponding to the area above the curve is the residual strain energy (referred to as residual energy), denoted as U *, and its value is:
Where V = LA is the volume of the rod; = P / A is the stress in the rod; = / L is the strain in the rod; 1, 1 is P1, respectively 1 corresponds to stress and strain. If the material of the rod is linear elastic (that is, the stress sum should become proportional), the strain energy and the residual energy are equal, that
Where E is the elastic modulus.
In a three-dimensional problem, there are six independent stress components and six independent strain components. In the case of small deformations, each stress component works on the corresponding strain component, so the expressions of strain energy and residual energy include six terms:
Where xx, yy, zz, xy, xz, yz is the stress component of the object during loading; xx, yy, zz, xy, xz, yz are the strain components corresponding to the above-mentioned stress components; the subscript 1 of the upper limit of the integration represents the end point of the load. For linear elastomers:
