A note on the derivation of quotient rules and their use in QR kinematics

QR kinematics have recently gained interest in various fields of mechanics due to its ease of application from an experimenter’s standpoint. This method, however, faces restriction owing to its dependence on the coordinate system in which the matrix of the deformation gradient is written and the QR decomposition is performed. Since different experimental setups are more amenable to different coordinate systems, it is important to derive and adopt transformation rules pertinent to QR kinematics that help us navigate from one coordinate system to another with ease. In this short technical note, the quotient rules for transforming vectors and second-order tensors between different coordinate systems obtained from a QR decomposition of the deformation gradient have been derived. The use of these quotient rules in comparing results obtained from two different rheometry methods has also been demonstrated.