Physical implications of decoupled boundary conditions in micropolar elasticity

The physical implications of boundary conditions in linearized micropolar elasticity are analyzed analytically and numerically. Firstly, a closed-form solution for the shearing of a block under arbitrary surface tractions, surface couple stresses, and volume loads is derived. This solution reveals the distinct physical roles of forces and couples, where forces primarily drive the displacement field and couples primarily drive the microrotation field, with the coupling parameter N controlling the strength of their interaction. Secondly, the torsion of a circular cylinder is analyzed, it is shown that the standard analytical solution implicitly couples a part of the microrotation to the macrorotation, which restricts the polar ratio to (Formula presented) for the ratio of micropolar to classical torsional rigidity to remain bounded as the cylinder diameter tends to zero. With numerical experiments it is demonstrated that this restriction is lifted when using decoupled micro-boundary conditions, and a pronounced size effect in torsional rigidity is recovered for the full admissible range (Formula presented), suggesting that the conventional identification of (Formula presented) is a consequence of the boundary condition prescription rather than an intrinsic material property.