278
P. Franciosi and M. Spagnuolo
Levin V. M. (1967). Thermal expansion coefficients for heterogeneous materials. Mekhanika
Tverdogo Tela, 2, 88–94 (English translation: Mechanics of Solids, 11, 58–61).
Li, J. Y., & Dunn, M. L. (1998). Micromechanics of magnetoelectroelastic composite materials:
Average fields and effective behaviour. Journal of Intelligent Material Systems and Structures,
9, 404–416.
Limodin, N., Salvo, L., Suery, M., & Di Michiel, M. (2007). In situ investigation by X-ray tomography of the overall and local microstructural changes occurring during partial remelting of an
Al–15.8 wt.% Cu alloy. Acta Materialia, 55, 3177–3191.
Liu, M. F. (2011). An exact deformation analysis for the magneto-electro-elastic fiber-reinforced
thin plate. Applied Mathematical Modeling, 35, 2443–2461.
Manolis, G. D., Makra, K., Dineva, P. S., & Rangelov, T. V. (2013). Seismic motions in a nonhomogeneous soil deposit with tunnels by a hybrid computational technique. Earthquakes and
Structures, 5(2), 161–205.
Masson, R., Bornert, M., Suquet, P., & Zaoui, A. (2000). An affine formulation for the prediction
of the effective properties of non linear composites and poly-crystals. Journal of the Mechanics
and Physics of Solids, 48(6/7), 1203–1227.
McCue, I., Ryan, S., Hemker, K., Xu, X., Li, N., Chen, M., et al. (2016). Size effects in the mechanical
properties of bulk bicontinuous ta/cu nanocomposites made by liquid metal dealloying. Advances
in Engineering Materials, 18(1), 46–50.
Michel, J. C., & Suquet, P. (2004). Computational analysis of nonlinear composite structures using
the non uniform transformation field analysis. Computer Methods in Applied Mechanics and
Engineering, 193, 5477–5502.
Mikata, Y. (2001). Explicit determination of piezo-electric Eshelby tensor for a spheroidal inclusion.
International Journal of Solids and Structures, 38, 7045–7063.
Mindlin, R. D. (1965). Second gradient of strain and surface-tension in linear elasticity. International
Journal of Solids and Structures, 1(4), 417–438.
Mori, T., & Tanaka, K. (1973). Average stressing the matrix and average elastic energy of materials
with misfitting inclusions. Acta Metallurgica, 21, 571–574.
Natterer, F. (1986). The mathematics of computerized tomography. Stuttgart: Teubner.
Norris, A. N. (1994). Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and
poroelastic solids. Proceedings of the Royal Society London A, 447, 175–188.
Pavese, M., Valle, M., & Badini, C. (2007). Effect of porosity of cordierite preforms on microstructure and mechanical strength of co-continuous ceramic composites. Journal of European Ceramic
Society, 27, 131–141.
Peng, H. X., Fan, Z., & Evans, J. R. G. (2001). Bi-continuous metal matrix composites. Materials
Science and Engineering A, 303, 37–45.
Pideri, C., & Seppecher, P. (1997). A second gradient material resulting from the homogenization
of an heterogeneous linear elastic medium. Continuum Mechanics and Thermodynamics, 9(5),
241–257.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für Angewandte Mathematik und Physik, 67(5), 121.
Placidi, L., Andreaus, U., & Giorgio, I. (2017). Identification of two-dimensional pantographic
structure via a linear D4 orthotropic second gradient elastic model. Journal of Engineering
Mathematics, 103(1), 1–21.
Placidi, L., Barchiesi, E., & Misra, A. (2018). A strain gradient variational approach to damage: A
comparison with damage gradient models and numerical results. Mathematics and Mechanics of
Complex Systems, 6(2), 77–100.
Placidi, L., Rosi, G., & Barchiesi, E. (2019). Analytical solutions of 2-dimensional second gradient
linear elasticity for Continua with cubic-D4 microstructure. In New Achievements in Continuum
Mechanics and Thermodynamics (pp. 383–401). Cham: Springer.
Poizat, C., & Sester, M. (1999). Effective properties of composites with embedded piezoelectric
fibres. Computational Materials Science, 16(1–4), 89–97.
P. Franciosi and M. Spagnuolo
Levin V. M. (1967). Thermal expansion coefficients for heterogeneous materials. Mekhanika
Tverdogo Tela, 2, 88–94 (English translation: Mechanics of Solids, 11, 58–61).
Li, J. Y., & Dunn, M. L. (1998). Micromechanics of magnetoelectroelastic composite materials:
Average fields and effective behaviour. Journal of Intelligent Material Systems and Structures,
9, 404–416.
Limodin, N., Salvo, L., Suery, M., & Di Michiel, M. (2007). In situ investigation by X-ray tomography of the overall and local microstructural changes occurring during partial remelting of an
Al–15.8 wt.% Cu alloy. Acta Materialia, 55, 3177–3191.
Liu, M. F. (2011). An exact deformation analysis for the magneto-electro-elastic fiber-reinforced
thin plate. Applied Mathematical Modeling, 35, 2443–2461.
Manolis, G. D., Makra, K., Dineva, P. S., & Rangelov, T. V. (2013). Seismic motions in a nonhomogeneous soil deposit with tunnels by a hybrid computational technique. Earthquakes and
Structures, 5(2), 161–205.
Masson, R., Bornert, M., Suquet, P., & Zaoui, A. (2000). An affine formulation for the prediction
of the effective properties of non linear composites and poly-crystals. Journal of the Mechanics
and Physics of Solids, 48(6/7), 1203–1227.
McCue, I., Ryan, S., Hemker, K., Xu, X., Li, N., Chen, M., et al. (2016). Size effects in the mechanical
properties of bulk bicontinuous ta/cu nanocomposites made by liquid metal dealloying. Advances
in Engineering Materials, 18(1), 46–50.
Michel, J. C., & Suquet, P. (2004). Computational analysis of nonlinear composite structures using
the non uniform transformation field analysis. Computer Methods in Applied Mechanics and
Engineering, 193, 5477–5502.
Mikata, Y. (2001). Explicit determination of piezo-electric Eshelby tensor for a spheroidal inclusion.
International Journal of Solids and Structures, 38, 7045–7063.
Mindlin, R. D. (1965). Second gradient of strain and surface-tension in linear elasticity. International
Journal of Solids and Structures, 1(4), 417–438.
Mori, T., & Tanaka, K. (1973). Average stressing the matrix and average elastic energy of materials
with misfitting inclusions. Acta Metallurgica, 21, 571–574.
Natterer, F. (1986). The mathematics of computerized tomography. Stuttgart: Teubner.
Norris, A. N. (1994). Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and
poroelastic solids. Proceedings of the Royal Society London A, 447, 175–188.
Pavese, M., Valle, M., & Badini, C. (2007). Effect of porosity of cordierite preforms on microstructure and mechanical strength of co-continuous ceramic composites. Journal of European Ceramic
Society, 27, 131–141.
Peng, H. X., Fan, Z., & Evans, J. R. G. (2001). Bi-continuous metal matrix composites. Materials
Science and Engineering A, 303, 37–45.
Pideri, C., & Seppecher, P. (1997). A second gradient material resulting from the homogenization
of an heterogeneous linear elastic medium. Continuum Mechanics and Thermodynamics, 9(5),
241–257.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für Angewandte Mathematik und Physik, 67(5), 121.
Placidi, L., Andreaus, U., & Giorgio, I. (2017). Identification of two-dimensional pantographic
structure via a linear D4 orthotropic second gradient elastic model. Journal of Engineering
Mathematics, 103(1), 1–21.
Placidi, L., Barchiesi, E., & Misra, A. (2018). A strain gradient variational approach to damage: A
comparison with damage gradient models and numerical results. Mathematics and Mechanics of
Complex Systems, 6(2), 77–100.
Placidi, L., Rosi, G., & Barchiesi, E. (2019). Analytical solutions of 2-dimensional second gradient
linear elasticity for Continua with cubic-D4 microstructure. In New Achievements in Continuum
Mechanics and Thermodynamics (pp. 383–401). Cham: Springer.
Poizat, C., & Sester, M. (1999). Effective properties of composites with embedded piezoelectric
fibres. Computational Materials Science, 16(1–4), 89–97.