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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.
- Angle of Twist
Factors affecting Angle of twist: The angle of twist in an...
- Angle of Twist
The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for stored energy will then be used to solve some elasticity problems using the energy methods mentioned in the previous section.
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.
It is evidently quite straightforward to extend a nonlinear small-strain finite element code to account for finite strains. The only changes necessary are: (1) The general finite deformation measures must be calculated; (2) The material tangent stiffness is now a function of strain;
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.
Based on these observations, we define the strain energy density of a solid as the work done per unit volume to deform a material from a stress free reference state to a loaded state. To write down an expression for the strain energy density, it is convenient to separate the strain into two parts . where, for an isotropic solid,
Find an expression for the strain energy density as a function of the position inside the plate, and draw the contour plot of the strain energy density function on the plate. If the thickness of the plate is 10mm, find the total strain energy stored inside the plate.
