Natural Strain & True Strain
When the true strain plastically under the stress of the deformation, the body changes permanently. It is assumed that no significant change in volume occurs due to loosening of the structure. This assumption is sufficiently accurate for all sheet metal materials. A change in length therefore requires a change in width and thickness.
The logarithmic true strain φ is called the natural strain :
- The direction of the transformation can be seen from the sign. Positive when the dimensions are increased (elongation) and negative when reduced (compression).
- Reversing the transformation results in the same absolute value
- The total degree of deformation of a multi-stage forming process results from the sum of the individual degrees of deformation
The direct and indirect costs of production are hidden in the degrees of forming. To optimize sheet metal constructions, it is therefore advisable to minimize local and global degrees of deformation as target variables.
The global natural strain of a deformed sheet can be calculated from the deformed area AU in relation to the initial area A0. The characteristic value φU can be used as a design variable in optimization algorithms. It can be easily determined in CAD and represents a minimization size.