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Article Dans Une Revue Applied Mathematical Modelling Année : 2011

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

Résumé

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=2/3 assumption or so called case 4, altogether case 1 (α=β=0 and γ=μLc2), case 2 α=0andβ=γ=1/2μLc2 and conformal case 3 α=-1/3μLc2andβ=γ=1/2 μLc2 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.
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hal-01176138 , version 1 (02-07-2018)

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Hamidréza Ramézani, Jena Jeong, Zhi-Qiang Feng. On parallel simulation of a new linear Cosserat elasticity model with grid framework model assumptions. Applied Mathematical Modelling, 2011, 35 (10), pp.4738--4758. ⟨10.1016/j.apm.2011.03.054⟩. ⟨hal-01176138⟩
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