Characterizing the non‐proportional and out‐of‐phase extent of tensor paths

Scalar measures are developed for characterizing the non‐proportional and out‐of‐phase extent of any symmetric second‐order tensor path. These scalar measures are constructed by introducing the concept of the principal axes of the tensor path. These measures are independent of the parameterization of the tensor path. As required these measures are invariant under coordinate transformations. For an example, these measures are used to characterize the stress history in the combustion dome of an internal‐combustion automotive engine.