How is true strain best defined?

True strain is defined as the ratio of the change in length to the instantaneous length. This definition accounts for the continuous change in the length of a material during deformation. Unlike engineering strain, which is based on the original length, true strain provides a more accurate representation of how materials behave under load, especially when significant deformation occurs.

In true strain calculation, as the material stretches and its length increases, the instantaneous length at any given moment reflects the current state of the material, allowing for more precise measurements of strain throughout the deformation process. This approach is particularly important in processes where large deformations are involved, ensuring that the effects of those deformations are captured accurately over time.

The other definitions do not capture the dynamic aspect of strain measurement since they either rely on the original length or do not consider the instantaneous changes in length that occur during the deformation process.