Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important.
The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) 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).
From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid:
a) is positive definite only when the discrepancy tensor is negative defined;
b) the non-local material symmetries are the same of the discrepancy tensor;
c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response.
Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/367875 |
| Date | January 2013 |
| Creators | Bacca, Mattia |
| Contributors | Bacca, Mattia, Bigoni, Davide |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | firstpage:1, lastpage:84, numberofpages:84 |
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