Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites Part I: Closed form expression for the effective higher-order constitutive tensor
By M. Bacca, Davide Bigoni, F. D. Corso, D. Veber. 2013
74 citations recorded by the source corpus.
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 are deferred to Part II of the present article.
Subfields: Materials Chemistry, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/422f127318bfc890e3c78521f354c688bec90ae2
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In Materials Chemistry
In Mechanics of Materials
Citations in the corpus
- Analysis of the tilted flat punch in couple-stress elasticity (2016, background): “Additionally, recent studies by Bigoni and Drugan (2007), and Bacca et al. (2013) provided an account of the determination of the couple-stress moduli via homogenization of heterogeneous materials.”
- Homogenization of periodic hexa- and tetrachiral cellular solids (2014, background): “…Sab, 1998) is available, there are considerations that limit its use (see Trinh et al., 2012) and suggest computational homogenization techniques based on second gradient continuum models (see Bacigalupo and Gambarotta, 2010, Bacca et al., 2013, Bacigalupo and Gambarotta, 2013, Bacigalupo, 2014).”