17 Microplane Modeling for Inelastic Responses …
325
a model for prediction of plastic and cyclic response of SMAs was developed. Some
austenitic and martensitic samples were fabricated by additive manufacturing, and
the specimens were examined under cyclic compressive loadings. The model was
validated in cyclic loadings as well, and the developed microplane formulation was
proved to be a reliable method in constitutive modeling of shape memory alloys.
The main benefit in application of microplane modeling is that 1-D responses are
just required to develop 3-D constitutive equations through the presented homogenization scheme. This not only reduces complexities of constitutive modeling but
also effectively assists in determining the required material parameters since only
1-D loadings need to be conducted. This technique has been utilized in many areas
and can be extended for several new applications in the future. For instance, the
presented approach is suitable for modeling particular classes of artificial materials,
such as metamaterials, which can possess extraordinary performance and properties
(Barchiesi et al. 2019; De Angelo et al. 2019; Yang et al. 2018; Alibert et al. 2003;
dell’Isola et al. 2016). Shape memory alloys can be employed in the structure of
such materials, and microplane theory can be applied to study various behaviors of
the products.
References
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1), 51–73.
Badel, P.-B., & Leblond, J.-B. (2003). A note on integration schemes for the microplane model of
the mechanical behaviour of concrete. Communications in Numerical Methods in Engineering,
20(1), 75–81.
Badnava, H., Mashayekhi, M., & Kadkhodaei, M. (2016). An anisotropic gradient damage model
based on microplane theory. International Journal of Damage Mechanics, 25(3), 336–357.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2019). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids, 24(1), 212–234.
Bažant, Z. P. (1984). Microplane model for strain controlled inelastic behavior. In C. S. Desai & R.
H. Gallagher (Eds.), Mechanics of Engineering Materials (pp. 45–59) Wiley.
Bažant, Z. P., & Di Luzio, G. (2004). Nonlocal microplane model with strain-softening yield limits.
International Journal of Solids and Structures, 41(24–25), 7209–7240.
Bažant, P., & Oh, B. (1986). Efficient numerical integration on the surface of a sphere. ZAMMJournal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und
Mechanik, 66(1), 37–49.
Bažant, Z. P., & Prat, P. C. (1987). Creep of anisotropic clay: New microplane model. Journal of
Engineering Mechanics, 113(7), 1050–1064.
Bažant, Z. P., & Prat, C. P. (1988a). Microplane model for brittle-plastic material: I. Theory. Journal
of Engineering Mechanics, 114(10), 1672–1688.
Bažant, Z., & Prat, P. (1988b). Microplane model for brittle plastic material: II. Verification. Journal
of Engineering Mechanics, 114(10), 1689–1699.
Bažant, Z. P., Xiang, Y., & Prat, P. C. (1996). Microplane model for concrete. I: Stress-strain
boundaries and finite strain. Journal of Engineering Mechanics, 122(3), 245–254.
Bažant, Z. P., & Zi, G. (2003). Microplane constitutive model for porous isotropic rocks.
International Journal for Numerical and Analytical Methods in Geomechanics, 27(1), 25–47.
325
a model for prediction of plastic and cyclic response of SMAs was developed. Some
austenitic and martensitic samples were fabricated by additive manufacturing, and
the specimens were examined under cyclic compressive loadings. The model was
validated in cyclic loadings as well, and the developed microplane formulation was
proved to be a reliable method in constitutive modeling of shape memory alloys.
The main benefit in application of microplane modeling is that 1-D responses are
just required to develop 3-D constitutive equations through the presented homogenization scheme. This not only reduces complexities of constitutive modeling but
also effectively assists in determining the required material parameters since only
1-D loadings need to be conducted. This technique has been utilized in many areas
and can be extended for several new applications in the future. For instance, the
presented approach is suitable for modeling particular classes of artificial materials,
such as metamaterials, which can possess extraordinary performance and properties
(Barchiesi et al. 2019; De Angelo et al. 2019; Yang et al. 2018; Alibert et al. 2003;
dell’Isola et al. 2016). Shape memory alloys can be employed in the structure of
such materials, and microplane theory can be applied to study various behaviors of
the products.
References
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1), 51–73.
Badel, P.-B., & Leblond, J.-B. (2003). A note on integration schemes for the microplane model of
the mechanical behaviour of concrete. Communications in Numerical Methods in Engineering,
20(1), 75–81.
Badnava, H., Mashayekhi, M., & Kadkhodaei, M. (2016). An anisotropic gradient damage model
based on microplane theory. International Journal of Damage Mechanics, 25(3), 336–357.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2019). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids, 24(1), 212–234.
Bažant, Z. P. (1984). Microplane model for strain controlled inelastic behavior. In C. S. Desai & R.
H. Gallagher (Eds.), Mechanics of Engineering Materials (pp. 45–59) Wiley.
Bažant, Z. P., & Di Luzio, G. (2004). Nonlocal microplane model with strain-softening yield limits.
International Journal of Solids and Structures, 41(24–25), 7209–7240.
Bažant, P., & Oh, B. (1986). Efficient numerical integration on the surface of a sphere. ZAMMJournal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und
Mechanik, 66(1), 37–49.
Bažant, Z. P., & Prat, P. C. (1987). Creep of anisotropic clay: New microplane model. Journal of
Engineering Mechanics, 113(7), 1050–1064.
Bažant, Z. P., & Prat, C. P. (1988a). Microplane model for brittle-plastic material: I. Theory. Journal
of Engineering Mechanics, 114(10), 1672–1688.
Bažant, Z., & Prat, P. (1988b). Microplane model for brittle plastic material: II. Verification. Journal
of Engineering Mechanics, 114(10), 1689–1699.
Bažant, Z. P., Xiang, Y., & Prat, P. C. (1996). Microplane model for concrete. I: Stress-strain
boundaries and finite strain. Journal of Engineering Mechanics, 122(3), 245–254.
Bažant, Z. P., & Zi, G. (2003). Microplane constitutive model for porous isotropic rocks.
International Journal for Numerical and Analytical Methods in Geomechanics, 27(1), 25–47.