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

摘要

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 = μL～2_c or ψ =2/3) assumption or so called case 4, altogether case 1 (α = β= 0 and γ = μL～2_c), case 2 (α = 0 and β = γ = 1/2μL～2_c) and con formal case 3 (α = -1/3μL～2_c and β = γ = 1/2μL～2_c) are examined by means of some numerical experiments for torsion test with a circular bar. The presence of m_33 (stress moment in z direction) on the top of specimen is confirmed numerically and analytically via a missing term (f_0Ωt(r x t(n)) ·δφds). By considering this term, m_33 is non-zero, whereas, the Dirich let boundary condition for displacements on the top of bar is used to apply the torque (M_T). 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 (L_c) 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.