Use of a rotation-invariant linear strain measure for linear elastic crack propagation calculations

The classical stress intensity factor concept requires linear elastic calculations based on infinitesimal strains in order to create the correct stress and strain singularity at the crack tip. Infinitesimal strains, however, are not rotation-invariant and cannot be used in structures undergoing large rotations even if the stretch is small. Therefore, a new strain measure is proposed based on a linearization of the Lagrange strain tensor written in terms of the right stretch tensor instead of the deformation gradient. In that way the local rotation is removed from the linear strain measure. An example of crack propagation of a rotating beam shows the effectiveness of the method.

Automated summary

The classical stress intensity factor concept, based on linear elastic calculations with infinitesimal strains, requires revisions when dealing with structures undergoing large rotations. A new strain measure based on the right stretch tensor is proposed to address this issue, effectively removing the local rotation from the linear strain measure. An example of crack propagation in a rotating beam demonstrates the effectiveness of this method.