References
Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions (National Bureau of Standards — Applied Mathematics Series 55, Washington D.C.).
Achour, M.; Bignonnet, F.; Barthélémy, J.-F.; Rozière, E. and Amiri, O. (2020). Multi-scale modeling of the chloride diffusivity and the elasticity of Portland cement paste. Construction and Building Materials 234, 117124.
Adessina, A.; Barthélémy, J.-F.; Lavergne, F. and Ben Fraj, A. (2017). Effective elastic properties of materials with inclusions of complex structure. International Journal of Engineering Science 119, 1–15.
Anderson, D. G. (1965). Iterative procedures for nonlinear integral equations. Journal of the ACM 12, 547–560.
Backus, G. E. (1962). Long-wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research 67, 4427–4440.
Barnett, D. M. and Asaro, R. J. (1972). The fracture mechanics of slit-like cracks in anisotropic elastic media. Journal of the Mechanics and Physics of Solids 20, 353–366.
Barthélémy, J.-F. (2009). Compliance and Hill polarization tensor of a crack in an anisotropic matrix. International Journal of Solids and Structures 46, 4064–4072.
Barthélémy, J.-F. (2009). Effective permeability of media with a dense network of long and micro fractures. Transport in Porous Media 76, 153–178.
Barthélémy, J.-F. (2020). Simplified approach to the derivation of the relationship between Hill polarization tensors of transformed problems and applications. International Journal of Engineering Science 154, 103326.
Barthélémy, J.-F. and Bignonnet, F. (2020). 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.
Barthélémy, J.-F. and Daniel, J.-M. (2011). Multiscale hydromechanical coupling for finite-element simulations of fractured reservoirs. In: 45th U.S. Rock Mechanics / Geomechanics Symposium, 11-557 of ARMA (San Francisco, CA, USA).
Barthélémy, J.-F.; Giraud, A.; Lavergne, F. and Sanahuja, J. (2016). The Eshelby inclusion problem in ageing linear viscoelasticity. International Journal of Solids and Structures 97–98, 530–542.
Barthélémy, J.-F.; Giraud, A.; Sanahuja, J. and Sevostianov, I. (2019). Effective properties of ageing linear viscoelastic media with spheroidal inhomogeneities. International Journal of Engineering Science 144, 103104.
Barthélémy, J.-F.; Sevostianov, I. and Giraud, A. (2021). Micromechanical modeling of a cracked elliptically orthotropic medium. International Journal of Engineering Science 161, 103454.
Barthélémy, J.-F. (2005). Approche micromécanique de la rupture et de la fissuration dans les géomatériaux. Ph.D. Thesis, École Nationale des Ponts et Chaussées.
Barthélémy, J.-F. (2026). Displacement and stress intensity factors of elliptical and ribbon-like cracks in a transformed transversely isotropic matrix. International Journal of Solids and Structures 341, 114293.
Barthélémy, J.-F. (2026). Echoes: Extended Calculator of HOmogEnization Schemes.
Barthélémy, J.-F. and Dormieux, L. (2003). Détermination du critère de rupture macroscopique d'un milieu poreux par homogénéisation non linéaire. Comptes Rendus. Mécanique 331, 271–276.
Barthélémy, J.-F.; Sevostianov, I.; Giraud, A. and Vilchevskaya, E. (2023). Compliance of a crack embedded in a transformed transversely isotropic material. Mathematics and Mechanics of Solids 29, 2538–2567.
Benveniste, Y. (1987). A new approach to the application of Mori-Tanaka's theory in composite materials. Mechanics of Materials 6, 147–157.
Benveniste, Y. and Miloh, T. (1986). The effective conductivity of composites with imperfect thermal contact at constituent interfaces. International Journal of Engineering Science 24, 1537–1552.
Berveiller, M. and Zaoui, A. (1978). An extension of the self-consistent scheme to plastically-flowing polycrystals. Journal of the Mechanics and Physics of Solids 26, 325–344.
Berveiller, M.; Fassi-Fehri, O. and Hihi, A. (1987). The problem of two plastic and heterogeneous inclusions in an anisotropic medium. International Journal of Engineering Science 25, 691–709.
Bishop, J. F. and Hill, R. (1951). A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42, 414–427.
Brenner, R.; Masson, R.; Castelnau, O. and Zaoui, A. (2002). A ``quasi-elastic'' affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites. European Journal of Mechanics - A/Solids 21, 943–960.
Brisard, S.; Bertin, M. and Legoll, F. (2023). A variance reduction strategy for numerical random homogenization based on the equivalent inclusion method. Computer Methods in Applied Mechanics and Engineering 416, 116389.
Brisard, S.; Dormieux, L. and Sab, K. (2014). A variational form of the equivalent inclusion method for numerical homogenization. International Journal of Solids and Structures 51, 716–728.
Brisard, S.; Sab, K. and Dormieux, L. (2013). New boundary conditions for the computation of the apparent stiffness of statistical volume elements. Journal of the Mechanics and Physics of Solids 61, 2638–2658.
Budiansky, B. (1965). On the elastic moduli of some heterogeneous materials. Journal of the Mechanics and Physics of Solids 13, 223–227.
Budiansky, B. and O'Connell, R. J. (1976). Elastic moduli of a cracked solid. International Journal of Solids and Structures 12, 81–97.
Cailletaud, G. and Pilvin, P. (1994). Utilisation de modèles polycristallins pour le calcul par éléments finis. Revue Européenne des Éléments Finis 3, 515–541.
Chen, F.; Sevostianov, I.; Giraud, A. and Grgic, D. (2015). Evaluation of the effective elastic and conductive properties of a material containing concave pores. International Journal of Engineering Science 97, 60–68.
Christensen, R. M. (1990). A critical evaluation for a class of micro-mechanics models. Journal of the Mechanics and Physics of Solids 38, 379–404.
Christensen, R. M. and Lo, K. H. (1979). Solutions for effective shear properties in three phase sphere and cylinder models. Journal of the Mechanics and Physics of Solids 27, 315–330.
Deudé, V.; Dormieux, L.; Kondo, D. and Maghous, S. (2002). Micromechanical approach to nonlinear poroelasticity: application to cracked rocks. Journal of Engineering Mechanics 128, 848–855.
Doghri, I. and Ouaar, A. (2003). Homogenization of two-phase elasto-plastic composite materials and structures. International Journal of Solids and Structures 40, 1681–1712.
Dormieux, L.; Jeannin, L.; Bemer, E.; Le, T. H. and Sanahuja, J. (2010). Micromechanical models of the strength of a sandstone. International Journal for Numerical and Analytical Methods in Geomechanics 34, 249–271.
Dormieux, L. and Kondo, D. (2016). Micromechanics of Fracture and Damage (Wiley).
Dormieux, L.; Kondo, D. and Ulm, F.-J. (2006). A micromechanical analysis of damage propagation in fluid-saturated cracked media. Comptes Rendus. Mécanique 334, 440–446.
Dormieux, L.; Lemarchand, E. and Brisard, S. (2016). Equivalent Inclusion Approach for Micromechanics Estimates of Nanocomposite Elastic Properties. Journal of Nanomechanics and Micromechanics 6, 04016002.
Dormieux, L.; Lemarchand, E. and Sanahuja, J. (2006). Comportement macroscopique des matériaux poreux à microstructure en feuillets. Comptes Rendus. Mécanique 334, 304–310.
Duan, H. L.; Wang, J.; Huang, Z. P. and Zhong, Y. (2005). Stress fields of a spheroidal inhomogeneity with an interphase in an infinite medium under remote loadings. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, 1055–1080.
Dvorak, G. J. and Benveniste, Y. (1992). On transformation strains and uniform fields in multiphase elastic media. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 437, 291–310.
Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 241, 376–396.
Espelid, T. O. and Genz, A. (1994). DECUHR: an algorithm for automatic integration of singular functions over a hyperrectangular region. Numerical Algorithms 8, 201–220.
Gavazzi, A. C. and Lagoudas, D. C. (1990). On the numerical evaluation of Eshelby's tensor and its application to elastoplastic fibrous composites. Computational Mechanics 7, 13–19.
Germain, P.; Nguyen, Q. S. and Suquet, P. (1983). Continuum thermodynamics. Journal of Applied Mechanics 50, 1010–1020.
Ghahremani, F. (1977). Numerical evaluation of the stresses and strains in ellipsoidal inclusions in an anisotropic elastic material. Mechanics Research Communications 4, 89–91.
Giraud, A.; Sevostianov, I.; Kushch, V. I.; Cosenza, P.; Prêt, D.; Barthélémy, J.-F. and Trofimov, A. (2019). Effective electrical conductivity of transversely isotropic rocks with arbitrarily oriented ellipsoidal inclusions. Mechanics of Materials 133, 174–192.
Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A 221, 163–198.
Gurson, A. L. (1977). 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.
Hashin, Z. and Shtrikman, S. (1962). A variational approach to the theory of the elastic behaviour of polycrystals. Journal of the Mechanics and Physics of Solids 10, 343–352.
Hashin, Z. and Shtrikman, S. (1963). A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 11, 127–140.
Hervé, E. and Zaoui, A. (1993), n-layered inclusion-based micromechanical modelling. International Journal of Engineering Science 31, 1–10.
Hervé-Luanco, E. (2014). 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.
Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. Second Edition (Society for Industrial and Applied Mathematics, Philadelphia).
Hill, R. (1952). The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A 65, 349–354.
Hill, R. (1965). A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 13, 213–222.
Hill, R. (1965). Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids 13, 89–101.
Hill, R. (1963). Elastic properties of reinforced solids: Some theoretical principles. Journal of the Mechanics and Physics of Solids 11, 357–372.
Hoenig, A. (1978). The behavior of a flat elliptical crack in an anisotropic elastic body. International Journal of Solids and Structures 14, 925–934.
Irwin, G. R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics 24, 361–364.
Kachanov, M. (1992). Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Reviews 45, 304–335.
Kachanov, M. and Sevostianov, I. (2018). Micromechanics of Materials, with Applications. Vol. 249 of Solid Mechanics and its Applications (Springer).
Kachanov, M. (1993). Elastic solids with many cracks and related problems. Advances in Applied Mechanics 30, 259–445.
Kanaun, S. K. (1981). Self-consistent field approximation for an elastic medium with isolated cracks. Prikladnaya Matematika i Mekhanika 45, 361–370.
Kanaun, S. K. and Levin, V. M. (2009). Elliptical cracks arbitrarily oriented in 3D-anisotropic elastic media. International Journal of Engineering Science 47, 777–792.
Kanaun, S. K. and Levin, V. M. (2009). Self-Consistent Methods for Composites — Vol. 1: Static Problems (Springer).
Kapitza, P. L. (1941). Heat Transfer and Superfluidity of Helium II. Physical Review 60, 354–355.
Kassir, M. K. and Sih, G. C. (1968). Three-dimensional stresses around elliptical cracks in transversely isotropic solids. Engineering Fracture Mechanics 1, 327–345.
Kellogg, O. D. (1929). Foundations of Potential Theory (Springer-Verlag, Berlin).
Kreher, W. (1990). Residual stresses and stored elastic energy of composites and polycrystals. Journal of the Mechanics and Physics of Solids 38, 115–128.
Kröner, E. (1961). Zur plastischen Verformung des Vielkristalls. Acta Metallurgica 9, 155–161.
Kunin, I. A. (1983). Elastic Media with Microstructure II: Three-Dimensional Models (Springer-Verlag, Berlin, Heidelberg).
Kushch, V. I.; Sevostianov, I. and Belyaev, A. S. (2015). Effective conductivity of spheroidal particle composite with imperfect interfaces: Complete solutions for periodic and random micro structures. Mechanics of Materials 89, 1–11.
Königsberger, M.; Pichler, B. and Hellmich, C. (2013). How do Porous Interfacial Transition Zones (ITZ) Trigger Elastic Limits of Concrete? — Micromechanics of ITZ Failure and ITZ-Aggregate Separation. In: Poromechanics V (American Society of Civil Engineers); pp. 1847–1856.
Königsberger, M.; Pichler, B. and Hellmich, C. (2014). Micromechanics of ITZ–Aggregate Interaction in Concrete Part I: Stress Concentration. Journal of the American Ceramic Society 97, 535–542.
Königsberger, M.; Pichler, B. and Hellmich, C. (2014). Micromechanics of ITZ-Aggregate Interaction in Concrete Part II: Strength Upscaling. Journal of the American Ceramic Society 97, 543–551.
Latyshev, A.; Bleyer, J.; Maurini, C. and Hale, J. (2025). Expressing general constitutive models in FEniCSx using external operators and algorithmic automatic differentiation. Journal of Theoretical, Computational and Applied Mechanics.
Lavergne, F.; Ben Fraj, A.; Bayane, I. and Barthélémy, J.-F. (2018). Estimating the mechanical properties of hydrating blended cementitious materials: An investigation based on micromechanics. Cement and Concrete Research 104, 37–60.
Laws, N. (1977). A note on interaction energies associated with cracks in anisotropic solids. Philosophical Magazine 36, 367–372.
Lebensohn, R. A. and Tomé, C. N. (1993). A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metallurgica et Materialia 41, 2611–2624.
Levin, V. M. (1967). On the Coefficients of Thermal Expansion of Heterogeneous Materials. Mechanics of Solids 2, 58–61. English translation of the Russian original.
Levin, V. M. (1967). О коэффициентах теплового расширения неоднородных материалов. Известия Академии наук СССР. Механика твердого тела 2, 88–94.
Maalej, Y.; Dormieux, L. and Sanahuja, J. (2009). Micromechanical approach to the failure criterion of granular media. European Journal of Mechanics – A/Solids 28, 647–653.
Maghous, S.; Dormieux, L. and Barthélémy, J.-F. (2009). Micromechanical approach to the strength properties of frictional geomaterials. European Journal of Mechanics - A/Solids 28, 179–188.
Martin, A.; Brisard, S.; Deleville, S. and Sab, K. (2023). Assessment of the equivalent inclusion method for the numerical homogenization of fibrous composites. Journal of Computational Physics 477, 111943.
Masson, R.; Bornert, M.; Suquet, P. and Zaoui, A. (2000). An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. Journal of the Mechanics and Physics of Solids 48, 1203–1227.
Masson, R. (2008). New explicit expressions of the Hill polarization tensor for general anisotropic elastic solids. International Journal of Solids and Structures 45, 757–769.
Miloh, T. and Benveniste, Y. (1999). On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces. Proceedings of the Royal Society of London A 455, 2687–2706.
Molinari, A.; Canova, G. R. and Ahzi, S. (1987). A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metallurgica 35, 2983–2994.
Molinari, A. and El Mouden, M. (1996). The problem of elastic inclusions at finite concentration. International Journal of Solids and Structures 33, 3131–3150.
Mori, T. and Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21, 571–574.
Moschovidis, Z. A. and Mura, T. (1975). Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method. Journal of Applied Mechanics 42, 847–852.
Mura, T. (1987). Micromechanics of Defects in Solids. 2 Edition (Martinus Nijhoff).
Méric, L.; Poubanne, P. and Cailletaud, G. (1991). Single crystal modeling for structural calculations: Part 1—Model presentation. Journal of Engineering Materials and Technology 113, 162–170.
Norris, A. N. (1985). A differential scheme for the effective moduli of composites. Mechanics of Materials 4, 1–16.
Ortiz, M. and Stainier, L. (1999). The variational formulation of viscoplastic constitutive updates. Computer Methods in Applied Mechanics and Engineering 171, 419–444.
Parnell, W. J. (2016). The Eshelby, Hill, Moment and Concentration Tensors for Ellipsoidal Inhomogeneities in the Newtonian Potential Problem and Linear Elastostatics. Journal of Elasticity 125, 231–294.
Parrott, L. J. and Killoh, D. C. (1984). Prediction of cement hydration. In: British Ceramic Proceedings, No. 35; pp. 41–53.
Pichler, B. and Hellmich, C. (2011). Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model. Cement and Concrete Research 41, 467–476.
Pierard, O. and Doghri, I. (2006). An enhanced affine formulation and the corresponding numerical algorithms for the mean-field homogenization of elasto-viscoplastic composites. International Journal of Plasticity 22, 131–157.
Ponte Castañeda, P. (1991). The effective mechanical properties of nonlinear isotropic composites. Journal of the Mechanics and Physics of Solids 39, 45–71.
Ponte Castañeda, P. (1996). Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. Journal of the Mechanics and Physics of Solids 44, 827–862.
Ponte Castañeda, P. and Willis, J. R. (1995). The effect of spatial distribution on the effective behavior of composite materials and cracked media. Journal of the Mechanics and Physics of Solids 43, 1919–1951.
Pouya, A. (2000). Une transformation du problème d'élasticité linéaire en vue d'application au problème de l'inclusion et aux fonctions de Green. Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics 328, 437–443.
Pouya, A. and Zaoui, A. (2006). A transformation of elastic boundary value problems with application to anisotropic behavior. International Journal of Solids and Structures 43, 4937–4956.
Powers, T. C. and Brownyard, T. L. (1946). 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. Nine-part series, Oct. 1946 – Apr. 1947; reprinted as Portland Cement Association Bulletin No. 22, 1948. Predates DOI assignment.
Reuss, A. (1929). Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 9, 49–58.
Rice, J. R. (1989). Weight function theory for three-dimensional elastic crack analysis. ASTM STP 1020, 29–57.
Rosen, B. W. and Hashin, Z. (1970). Effective thermal expansion coefficients and specific heats of composite materials. International Journal of Engineering Science 8, 157–173.
Sanahuja, J. (2013). Effective behaviour of ageing linear viscoelastic composites: Homogenization approach. International Journal of Solids and Structures 50, 2846–2856.
Sanahuja, J.; Dormieux, L. and Chanvillard, G. (2007). Modelling elasticity of a hydrating cement paste. Cement and Concrete Research 37, 1427–1439.
Sevostianov, I. and Kachanov, M. (2002). Explicit cross-property correlations for anisotropic two-phase composite materials. Journal of the Mechanics and Physics of Solids 50, 253–282.
Sevostianov, I. and Kachanov, M. (2007). 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.
Sevostianov, I. (2014). On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites. Mechanics of Materials 75, 45–59.
Sevostianov, I.; Chen, F.; Giraud, A. and Grgic, D. (2016). Compliance and resistivity contribution tensors of axisymmetric concave pores. International Journal of Engineering Science 101, 14–28.
Sevostianov, I. and Giraud, A. (2013). Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape. International Journal of Engineering Science 64, 23–36.
Sevostianov, I. and Kachanov, M. (2011). Elastic fields generated by inhomogeneities: Far-field asymptotics, its shape dependence and relation to the effective elastic properties. International Journal of Solids and Structures 48, 2340–2348.
Sevostianov, I.; Yilmaz, N.; Kushch, V. and Levin, V. (2005). Effective elastic properties of matrix composites with transversely-isotropic phases. International Journal of Solids and Structures 42, 455–476.
Simo, J. C. and Hughes, T. J. (1998). Computational Inelasticity. Interdisciplinary Applied Mathematics (Springer, New York).
Simo, J. C. and Taylor, R. L. (1985). Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering 48, 101–118.
Somé, S. C.; Barthélémy, J.-F.; Mouillet, V.; Hammoum, F. and Liu, G. (2022). 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.
Suquet, P. (1997). Effective Properties of Nonlinear Composites. In: Continuum Micromechanics (Springer Vienna); pp. 197–264.
Suvorov, A. P. and Dvorak, G. J. (2002). Rate form of the Eshelby and Hill tensors. International Journal of Solids and Structures 39, 5659–5678.
Sævik, P. N.; Jakobsen, M.; Lien, M. and Berre, I. (2014). Anisotropic effective conductivity in fractured rocks by explicit effective medium methods. Geophysical Prospecting 62, 1297–1314.
Tennis, P. D. and Jennings, H. M. (2000). A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes. Cement and Concrete Research 30, 855–863.
Voigt, W. (1889). Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Annalen der Physik 274, 573–587.
Walpole, L. J. (1981). Elastic Behavior of Composite Materials: Theoretical Foundations. In: Advances in Applied Mechanics, Vol. 21 (Elsevier); pp. 169–242.
Walsh, J. B. (1965). The effect of cracks on the compressibility of rock. Journal of Geophysical Research 70, 381–389.
Willis, J. R. (1968). The stress field around an elliptical crack in an anisotropic elastic medium. International Journal of Engineering Science 6, 253–263.
Willis, J. R. (1977). Bounds and self-consistent estimates for the overall properties of anisotropic composites. Journal of the Mechanics and Physics of Solids 25, 185–202.
Willis, J. R. (1982). Elasticity theory of composites. In: Mechanics of Solids — The Rodney Hill 60th Anniversary Volume (Pergamon Press); pp. 653–686.
Withers, P. J. (1989). The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium, and its relevance to composite materials. Philosophical Magazine A 59, 759–781.
Zeller, R. and Dederichs, P. H. (1973). Elastic Constants of Polycrystals. Physica Status Solidi B 55, 831–842.