On the influence of the microstructure in the calculation of shear intensity factors

In beam theory shear intensity factors are related to the additional bending deformations due to the nonuniform distribution of the shear stresses on the cross section. In classical beam theory, this is taken into account by the introduction of the so called Timoshenko’s constant which depends on the geometry and on Poisson’s ratio. In a recent work, starting from three - dimensional elasticity and using asymptotic analysis methods Trabucho and Viano [ 1 ] have shown that Timoshenko’s constant should be replaced by a matrix function whose diagonal terms reduce to the classical constant for special geometries and loadings. In this work, we extend these results to a class of multicellular cross sections and/or finely perforated materials. We introduce together with the asymptotic expansion method, homogenization techniques and we give a definition of the new shear intensity matrix for the homogenized material clearly showing its dependence on the loading, the geometry, Poisson’s ratio and the microstructure.