Particle stresslet tensor ($S=-\mathrm{sym}{\int }_A\mathbf{x}(\mathbf{\sigma }\mathbf{n})dS$)

The symmetric first moment of the traction exerted by a rigid inclusion, with the surface normal pointing into the inclusion. Its contraction with the background rate-of-strain tensor is the strain-related contribution to extra dissipation due to a rigid inclusion. A trace-free version is equivalent for an incompressible flow. This tensor is distinct from the axisymmetric force-dipole flow used as a far-field singularity.