Abstract:  It is shown that second-order homogenization of a Cauchy-elastic dilute suspension of randomly distributed inclusions yields an equivalent second gradient (Mindlin) elastic material. This result is valid for both plane and three-dimensional problems and extends earlier findings by Bigoni and Drugan [Bigoni, D., Drugan, W.J., 2007. Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech. 74, 741–753] from several points of view: (i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; (ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; (iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). The constitutive higher-order tensor defining the equivalent Mindlin solid is given in a surprisingly simple formula. Applications, treatment of material symmetries and positive definiteness of the effective higher-order constitutive tensor will be explained in the final part of this work.

Biosketch:  After graduating in Civil Engineering at the University of Trento in 2005, Dr. Mattia Bacca took a master degree in Structural Engineering in 2009. His accademic career started with a PhD program in Mechanical and Structural Engineering in the same university with Professor Davide Bigoni. He defended his thesis at the end of April 2013 and the 16th of May 2013 he started a post doctoral project in Mechanical Engineering at UCSB with Professor Robert McMeeking.

Host: Prof. Frederic Gibou