References

All bibliographic references used across the MeanFieldHom.jl documentation are collected here. Individual chapters cite entries by their BibTeX key via the [key](@cite) syntax — this page renders the full list.

[1]: L. J. Walpole. Elastic Behavior of Composite Materials: Theoretical Foundations. In: Advances in Applied Mechanics, Vol. 21 (Elsevier, 1981); pp. 169–242.
[2]: J.-F. Barthélémy. Simplified approach to the derivation of the relationship between Hill polarization tensors of transformed problems and applications. International Journal of Engineering Science 154, 103326 (2020).
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[6]: A. Adessina, J.-F. Barthélémy, F. Lavergne and A. Ben Fraj. Effective elastic properties of materials with inclusions of complex structure. International Journal of Engineering Science 119, 1–15 (2017).
[7]: J.-F. Barthélémy, A. Giraud, F. Lavergne and J. Sanahuja. The Eshelby inclusion problem in ageing linear viscoelasticity. International Journal of Solids and Structures 97–98, 530–542 (2016).
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[29]: A. N. Norris. A differential scheme for the effective moduli of composites. Mechanics of Materials 4, 1–16 (1985).
[30]: J.-F. Barthélémy. Displacement and stress intensity factors of elliptical and ribbon-like cracks in a transformed transversely isotropic matrix, in preparation.
[31]: M. Kachanov. Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Reviews 45, 304–335 (1992).
[32]: M. Kachanov. Elastic solids with many cracks and related problems. Advances in Applied Mechanics 30, 259–445 (1993).
[33]: J.-F. Barthélémy, I. Sevostianov, A. Giraud and E. Vilchevskaya. Compliance of a crack embedded in a transformed transversely isotropic material. Mathematics and Mechanics of Solids 29, 2538–2567 (2023).
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[37]: J.-F. Barthélémy, I. Sevostianov and A. Giraud. Micromechanical modeling of a cracked elliptically orthotropic medium. International Journal of Engineering Science 161, 103454 (2021).
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[43]: J. R. Rice. Weight function theory for three-dimensional elastic crack analysis. ASTM STP 1020, 29–57 (1989).
[44]: S. K. Kanaun. Self-consistent field approximation for an elastic medium with isolated cracks. Prikladnaya Matematika i Mekhanika 45, 361–370 (1981).
[45]: I. A. Kunin. Elastic Media with Microstructure II: Three-Dimensional Models (Springer-Verlag, Berlin, Heidelberg, 1983).
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[49]: E. Hervé-Luanco. Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites. International Journal of Solids and Structures 51, 2865–2877 (2014).
[50]: J.-F. Barthélémy and F. Bignonnet. The Eshelby problem of the confocal N-layer spheroid with imperfect interfaces and the notion of equivalent particle in thermal conduction. International Journal of Engineering Science 150, 103274 (2020).
[51]: P. L. Kapitza. Heat Transfer and Superfluidity of Helium II. Physical Review 60, 354–355 (1941).
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[55]: J.-F. Barthélémy, A. Giraud, J. Sanahuja and I. Sevostianov. Effective properties of ageing linear viscoelastic media with spheroidal inhomogeneities. International Journal of Engineering Science 144, 103104 (2019).
[56]: J. Sanahuja. Effective behaviour of ageing linear viscoelastic composites: Homogenization approach. International Journal of Solids and Structures 50, 2846–2856 (2013).
[57]: J.-F. Barthélémy. Echoes: Extended Calculator of HOmogEnization Schemes (Nov 2022).
[58]: I. Sevostianov and M. Kachanov. Effect of interphase layers on the overall elastic and conductive properties of matrix composites. Applications to nanosize inclusion. International Journal of Solids and Structures 44, 1304–1315 (2007).
[59]: P. Suquet. Effective Properties of Nonlinear Composites. In: Continuum Micromechanics (Springer Vienna, 1997); pp. 197–264.
[60]: P. Ponte Castañeda. The effective mechanical properties of nonlinear isotropic composites. Journal of the Mechanics and Physics of Solids 39, 45–71 (1991).
[61]: W. Kreher. Residual stresses and stored elastic energy of composites and polycrystals. Journal of the Mechanics and Physics of Solids 38, 115–128 (1990).
[62]: A. L. Gurson. Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media. Journal of Engineering Materials and Technology 99, 2–15 (1977).
[63]: J. Sanahuja, L. Dormieux and G. Chanvillard. Modelling elasticity of a hydrating cement paste. Cement and Concrete Research 37, 1427–1439 (2007).
[64]: T. C. Powers and T. L. Brownyard. Studies of the physical properties of hardened Portland cement paste. Journal of the American Concrete Institute (Proceedings) 43, 101–132, 249–336, 469–504, 549–602, 669–712, 845–880, 933–992 (1946). Nine-part series, Oct. 1946 – Apr. 1947; reprinted as Portland Cement Association Bulletin No. 22, 1948. Predates DOI assignment.
[65]: P. D. Tennis and H. M. Jennings. A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes. Cement and Concrete Research 30, 855–863 (2000).
[66]: M. Achour, F. Bignonnet, J.-F. Barthélémy, E. Rozière and O. Amiri. Multi-scale modeling of the chloride diffusivity and the elasticity of Portland cement paste. Construction and Building Materials 234, 117124 (2020).
[67]: B. Pichler and C. Hellmich. Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model. Cement and Concrete Research 41, 467–476 (2011).
[68]: M. Königsberger, B. Pichler and C. Hellmich. How do Porous Interfacial Transition Zones (ITZ) Trigger Elastic Limits of Concrete? — Micromechanics of Concrete. In: Poromechanics V (American Society of Civil Engineers, 2013); pp. 1847–1856.
[69]: S. C. Somé, J.-F. Barthélémy, V. Mouillet, F. Hammoum and G. Liu. Effect of thermo-oxidative ageing on the rheological properties of bituminous binders and mixes: Experimental study and multi-scale modeling. Construction and Building Materials 344, 128260 (2022).