On parallel simulation of a new linear Cosserat elasticity model with grid framework model assumptions

In the present paper, the linear Cosserat elasticity involving the grid framework model for micro-rotations as boundary condition or side-condition has been taken into account. The identical micro-rotation constants α=β=γ=μLc2orΨ=23 assumption or so called case 4, altogether case 1 (α = β = 0 and γ=μLc2), case 2 α=0andβ=γ=12μLc2 and conformal case 3 α=-13μLc2andβ=γ=12μLc2 are examined by means of some numerical experiments for torsion test with a circular bar. The presence of m33 (stress moment in z   direction) on the top of specimen is confirmed numerically and analytically via a missing term ∫∂Ωt(r×t(n))·δϕdS. By considering this term, m33 is non-zero, whereas, the Dirichlet boundary condition for displacements on the top of bar is used to apply the torque (MT). The outcomes reveal that the case 4 as well as other cases is still bounded. This property is found out for curvature stiffness as well. These cases are presented in Torque-Log (Lc) diagram. In this diagram, two non-size affected zones (zones I and III) and one size affected zone would be inferred. By taking advantage of this curve, we can probably consider Cosserat theory as a multi-scale tool and some outlooks for a fresh experimental departure are discussed.