Use of a rotation-invariant linear strain measure for linear elastic crack propagation calculations. (15th April 2021) - Dhondt, Guido; Hackenberg, Hans-Peter
Abstract: 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. Highlights: Linearized strain is not invariant with respect to large rotations. Therefore, it cannot be used for fracture analyses subject to large rotations. For K-based calculations the Biot strain measure is proposed instead. An example of crack propagation in a hinged beam shows its effectiveness.