302
Z. Louna et al.
Goda, I., & Ganghoffer, J.-F. (2016). Construction of first and second order grade anisotropic
continuum media for 3D porous and textile composite structures. Composite Structures, 141,
292–327.
Goda, I., Ganghoffer, J. F., & Maurice, G. (2016). Combined bone internal and external remodeling
based on Eshelby stress. International Journal of Solids and Structures, 94–95, 138–157.
Goda, I., Rahouadj, R., & Ganghoffer, J.-F. (2013). Size dependent static and dynamic behavior
of trabecular bone based on micromechanical models of the trabecular. International Journal of
Engineering Science, 72, 53–77.
Harrigan, T. P., Jasty, M. J., Mann, R. W., & Harris, W. H. (1988). Limitations of the continuum
assumption in cancellous bone. Journal of Biomechanics, 21, 269–275.
Kröner, E. (1976). Elasticity theory of materials with long range cohesive forces. International
Journal of Solids and Structures, 3(5), 731–742.
Lakes, R. (1995). On the torsional properties of single osteons. Journal of Biomechanics, 28(1409–
1410), 1.
Lekszycki, T., & dell’Isola, F. (2012). A mixture model with evolving mass densities for describing
synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials.
ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik
und Mechanik, 92(6), 426–444.
Lemaitre, J., & Chaboche, J. L. (2009). Mécanique des matériaux solides. Paris: Dunod.
Louna, Z., Goda, I., & Ganghoffer, J. F. (2018). Identification of a constitutive law for trabecular
bone samples under remodeling in the framework of irreversible thermodynamics. Continuum
Mechanics and Thermodynamics, 30(3), 529–551.
Louna, Z., Goda, I., & Ganghoffer, J. F. (2019). Homogenized strain gradient remodeling model for
trabecular bone microstructures. Continuum Mechanics and Thermodynamics, 31(5), 1339–1367.
Madeo, A., George, D., Lekszycki, T., Nierenberger, M., & Rémond, Y. (2012). A second
gradient continuum model accounting for some effects of micro-structure on reconstructed bone
remodeling. Comptes Rendus Mécanique, 340(8), 575–589.
Madeo, A., Lekszycki, T., & dell’Isola, F. (2011). Continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery. Comptes
Rendus Mécanique, 339(10), 625–682.
Maugin, G. A. (1980). The method of virtual power in continuum mechanics: Application to coupled
fields. Acta Mechanica, 35, 1–70.
Olive, M., & Auffray, N. (2014). Isotropic invariants of a completely symmetric third-order tensor.
Journal of Mathematical Physics, American Institute of Physics (AIP), 55(9), 1.4895466.
Park, H. C., & Lakes, R. S. (1986). Cosserat micromechanics of human bone: Strain redistribution
by a hydration sensitive constituent. Journal of Biomechanics, 19(5), 385–397.
Ramézani, H., El-Hraiech, A., Jeong, J., & Benhamou, C.-L. (2012). Size effect method application
for modeling of human cancellous bone using geometrically exact Cosserat elasticity. Computer
Methods in Applied Mechanics and Engineering, 237, 227–243.
Reda, H., Goda, I., Ganghoffer, J. F., L’Hostis, G., & Lakiss, H. (2017). Dynamical analysis of
homogenized second gradient anisotropic media for textile composite structures and analysis of
size effects. Composite Structures, 161, 540–551.
Skalak, R., Farrow, D. A., & Hoger, A. (1997). Kinematics of surface growth. Journal of
Mathematical Biology, 35, 869–907.
Taylor, M., Cotton, J., & Zioupos, P. (2002). Finite element simulation of the fatigue behaviour of
cancellous bone. Meccanica, 37, 419–429.
Yang, J. F. C., & Lakes, R. S. (1982). Experimental study of micropolar and couple stress elasticity
in compact bone in bending. Journal of Biomechanics, 15(2), 91–98.
Z. Louna et al.
Goda, I., & Ganghoffer, J.-F. (2016). Construction of first and second order grade anisotropic
continuum media for 3D porous and textile composite structures. Composite Structures, 141,
292–327.
Goda, I., Ganghoffer, J. F., & Maurice, G. (2016). Combined bone internal and external remodeling
based on Eshelby stress. International Journal of Solids and Structures, 94–95, 138–157.
Goda, I., Rahouadj, R., & Ganghoffer, J.-F. (2013). Size dependent static and dynamic behavior
of trabecular bone based on micromechanical models of the trabecular. International Journal of
Engineering Science, 72, 53–77.
Harrigan, T. P., Jasty, M. J., Mann, R. W., & Harris, W. H. (1988). Limitations of the continuum
assumption in cancellous bone. Journal of Biomechanics, 21, 269–275.
Kröner, E. (1976). Elasticity theory of materials with long range cohesive forces. International
Journal of Solids and Structures, 3(5), 731–742.
Lakes, R. (1995). On the torsional properties of single osteons. Journal of Biomechanics, 28(1409–
1410), 1.
Lekszycki, T., & dell’Isola, F. (2012). A mixture model with evolving mass densities for describing
synthesis and resorption phenomena in bones reconstructed with bio-resorbable materials.
ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik
und Mechanik, 92(6), 426–444.
Lemaitre, J., & Chaboche, J. L. (2009). Mécanique des matériaux solides. Paris: Dunod.
Louna, Z., Goda, I., & Ganghoffer, J. F. (2018). Identification of a constitutive law for trabecular
bone samples under remodeling in the framework of irreversible thermodynamics. Continuum
Mechanics and Thermodynamics, 30(3), 529–551.
Louna, Z., Goda, I., & Ganghoffer, J. F. (2019). Homogenized strain gradient remodeling model for
trabecular bone microstructures. Continuum Mechanics and Thermodynamics, 31(5), 1339–1367.
Madeo, A., George, D., Lekszycki, T., Nierenberger, M., & Rémond, Y. (2012). A second
gradient continuum model accounting for some effects of micro-structure on reconstructed bone
remodeling. Comptes Rendus Mécanique, 340(8), 575–589.
Madeo, A., Lekszycki, T., & dell’Isola, F. (2011). Continuum model for the bio-mechanical interactions between living tissue and bio-resorbable graft after bone reconstructive surgery. Comptes
Rendus Mécanique, 339(10), 625–682.
Maugin, G. A. (1980). The method of virtual power in continuum mechanics: Application to coupled
fields. Acta Mechanica, 35, 1–70.
Olive, M., & Auffray, N. (2014). Isotropic invariants of a completely symmetric third-order tensor.
Journal of Mathematical Physics, American Institute of Physics (AIP), 55(9), 1.4895466.
Park, H. C., & Lakes, R. S. (1986). Cosserat micromechanics of human bone: Strain redistribution
by a hydration sensitive constituent. Journal of Biomechanics, 19(5), 385–397.
Ramézani, H., El-Hraiech, A., Jeong, J., & Benhamou, C.-L. (2012). Size effect method application
for modeling of human cancellous bone using geometrically exact Cosserat elasticity. Computer
Methods in Applied Mechanics and Engineering, 237, 227–243.
Reda, H., Goda, I., Ganghoffer, J. F., L’Hostis, G., & Lakiss, H. (2017). Dynamical analysis of
homogenized second gradient anisotropic media for textile composite structures and analysis of
size effects. Composite Structures, 161, 540–551.
Skalak, R., Farrow, D. A., & Hoger, A. (1997). Kinematics of surface growth. Journal of
Mathematical Biology, 35, 869–907.
Taylor, M., Cotton, J., & Zioupos, P. (2002). Finite element simulation of the fatigue behaviour of
cancellous bone. Meccanica, 37, 419–429.
Yang, J. F. C., & Lakes, R. S. (1982). Experimental study of micropolar and couple stress elasticity
in compact bone in bending. Journal of Biomechanics, 15(2), 91–98.