  Grain boundary (GB) migration stands as a linchpin process governing
microstructural evolution in polycrystalline materials. Over the past decade,
the concept of shear coupling, quantified through the shear coupling factor,
has transformed our understanding and driven the development of theoretical
frameworks for unifying GB behaviors. In this study, we introduced a novel
concept of shear coupling strength designed to overcome the limitations of the
conventional shear coupling factor, notably its deficiency in conveying
"coupling" information. The shear coupling tensor formed by the shear coupling
strengths characterizes intrinsic shear coupling properties across diverse GBs
and reveals complex dynamics within the GB mobility tensor. The molecular
dynamics simulation confirms the symmetry of the GB mobility tensor. This
symmetry is inherently built into the shear coupling strength, aligning with an
assumption made in previous studies. Additionally, an efficient methodology has
been developed for streamlined extraction of both shear coupling and GB
mobility tensors from atomistic simulations. This advancement holds the
potential to sample GB behavior across extensive datasets, significantly
enhancing our ability to predict structure-property relationships within the
expansive 5-parameter space of GBs.
