16 Strain Gradient Models for Growing Solid Bodies
301
Cosserat, E., & Cosserat, F. (1909). Théorie des Corps Déformables. Paris: Librairie Scientifique
A. Hermann et Fils.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015a). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8), 887–928.
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., … Hild,
F. (2019). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
dell’Isola, F., Seppecher, P., & Della Corte, A. (2015b). The postulations á la D’Alembert and á
la Cauchy for higher gradient continuum theories are equivalent: A review of existing results.
Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering
Sciences, 471, 2183.
Epstein, M., & Maugin, G. A. (2000). Thermomechanics of volumetric growth in uniform bodies.
International Journal of Plasticity, 16, 951–978.
Eremeyev, V. A. (2019). On non-holonomic boundary conditions within the nonlinear Cosserat
continuum. In New achievements in continuum mechanics and thermodynamics (pp. 93–104).
Cham: Springer.
Eringen, A. C., & Edelen, D. G. B. (1972). On nonlocal elasticity. International Journal of
Engineering Science, 10(3), 233–248.
Forest, S., & Sievert, R. (2003). Elastoviscoplastic constitutive frameworks for generalized continua.
Acta Mechanica, 160, 71–111.
Frasca, P., Harper, R., & Katz, J. L. (1981). Strain and frequency dependence of shear storage
modulus for human single osteons and cortical bone micro samples—Size and hydration effects.
Journal of Biomechanics, 14(10), 679–690.
Ganghoffer, J. F. (2010). Mechanical modeling of growth considering domain variation—Part II:
Volumetric and surface growth involving Eshelby tensors. Journal of the Mechanics and Physics
of Solids, 58(9), 1434–1459.
Ganghoffer, J. F., & Haussy, B. (2005). Mechanical modeling of growth considering domain variation. Part I: Constitutive framework. International Journal of Solids and Structures, 42(15),
4311–4337.
Ganghoffer, J. F., Plotnikov, P. I., & Sokołowski, J. (2014). Mathematical modeling of volumetric
material growth. Archive of Applied Mechanics, 84(9–11), 1357–1371.
Giorgio, I., Andreaus, U., dell’Isola, I., & Lekszycki, T. (2017). Viscous second gradient porous
materials for bones reconstructed with bio-resorbable grafts. Extreme Mechanics Letters, 13,
141–147.
Giorgio, I., Andreaus, U., & Madeo, A. (2016). The influence of different loads on the remodeling
process of a bone and bioresorbable material mixture with voids. Continuum Mechanics and
Thermodynamics, 28(1–2), 21–40.
Giorgio, I., De Angelo, M., Turco, E., & Misra, A. (2019). A Biot–Cosserat two-dimensional elastic
nonlinear model for a micromorphic medium. Continuum Mechanics and Thermodynamics, 1–13.
Goda, I., Assidi, M., Belouettar, S., & Ganghoffer, J.-F. (2012). A micropolar anisotropic constitutive
model of cancellous bone from discrete homogenization. Journal of the Mechanical Behavior of
Biomedical Materials, 16, 87–108.
Goda, I., Assidi, M., & Ganghoffer, J.-F. (2014). A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure. Biomechanics and Modeling
in Mechanobiology, 13, 53–83.
Goda, I., & Ganghoffer, J.-F. (2015a). 3D plastic collapse and brittle fracture surface models of
trabecular bone from asymptotic homogenization method. International Journal of Engineering
Science, 87, 58–82.
Goda, I., & Ganghoffer, J.-F. (2015b). Identification of couple-stress moduli of vertebral trabecular
bone based on the 3D internal architectures. Journal of the Mechanical Behavior of Biomedical
Materials, 51, 99–118.
301
Cosserat, E., & Cosserat, F. (1909). Théorie des Corps Déformables. Paris: Librairie Scientifique
A. Hermann et Fils.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015a). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8), 887–928.
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., … Hild,
F. (2019). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
dell’Isola, F., Seppecher, P., & Della Corte, A. (2015b). The postulations á la D’Alembert and á
la Cauchy for higher gradient continuum theories are equivalent: A review of existing results.
Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering
Sciences, 471, 2183.
Epstein, M., & Maugin, G. A. (2000). Thermomechanics of volumetric growth in uniform bodies.
International Journal of Plasticity, 16, 951–978.
Eremeyev, V. A. (2019). On non-holonomic boundary conditions within the nonlinear Cosserat
continuum. In New achievements in continuum mechanics and thermodynamics (pp. 93–104).
Cham: Springer.
Eringen, A. C., & Edelen, D. G. B. (1972). On nonlocal elasticity. International Journal of
Engineering Science, 10(3), 233–248.
Forest, S., & Sievert, R. (2003). Elastoviscoplastic constitutive frameworks for generalized continua.
Acta Mechanica, 160, 71–111.
Frasca, P., Harper, R., & Katz, J. L. (1981). Strain and frequency dependence of shear storage
modulus for human single osteons and cortical bone micro samples—Size and hydration effects.
Journal of Biomechanics, 14(10), 679–690.
Ganghoffer, J. F. (2010). Mechanical modeling of growth considering domain variation—Part II:
Volumetric and surface growth involving Eshelby tensors. Journal of the Mechanics and Physics
of Solids, 58(9), 1434–1459.
Ganghoffer, J. F., & Haussy, B. (2005). Mechanical modeling of growth considering domain variation. Part I: Constitutive framework. International Journal of Solids and Structures, 42(15),
4311–4337.
Ganghoffer, J. F., Plotnikov, P. I., & Sokołowski, J. (2014). Mathematical modeling of volumetric
material growth. Archive of Applied Mechanics, 84(9–11), 1357–1371.
Giorgio, I., Andreaus, U., dell’Isola, I., & Lekszycki, T. (2017). Viscous second gradient porous
materials for bones reconstructed with bio-resorbable grafts. Extreme Mechanics Letters, 13,
141–147.
Giorgio, I., Andreaus, U., & Madeo, A. (2016). The influence of different loads on the remodeling
process of a bone and bioresorbable material mixture with voids. Continuum Mechanics and
Thermodynamics, 28(1–2), 21–40.
Giorgio, I., De Angelo, M., Turco, E., & Misra, A. (2019). A Biot–Cosserat two-dimensional elastic
nonlinear model for a micromorphic medium. Continuum Mechanics and Thermodynamics, 1–13.
Goda, I., Assidi, M., Belouettar, S., & Ganghoffer, J.-F. (2012). A micropolar anisotropic constitutive
model of cancellous bone from discrete homogenization. Journal of the Mechanical Behavior of
Biomedical Materials, 16, 87–108.
Goda, I., Assidi, M., & Ganghoffer, J.-F. (2014). A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure. Biomechanics and Modeling
in Mechanobiology, 13, 53–83.
Goda, I., & Ganghoffer, J.-F. (2015a). 3D plastic collapse and brittle fracture surface models of
trabecular bone from asymptotic homogenization method. International Journal of Engineering
Science, 87, 58–82.
Goda, I., & Ganghoffer, J.-F. (2015b). Identification of couple-stress moduli of vertebral trabecular
bone based on the 3D internal architectures. Journal of the Mechanical Behavior of Biomedical
Materials, 51, 99–118.