A Rational Study on Limit States in Hypoelastic Materials

Document Type : Research Paper

Authors

1 School of Engineering, Shiraz University, Shiraz, Iran

2 Laboratoire Navier, École des Ponts ParisTech, Paris, France

Abstract

Despite the definition of failure being almost thoroughly studied in other theories such as elasto-plasticity, this paper studies the possibility of capturing or defining some limit states in hypoelastic materials. It is shown that for many hypoelastic materials the limit state, as a notion of failure, can take the place of the yield or failure in classical plasticity. The procedure is general, and all equations are rational, i.e. they are not dependent on a particular form of a constitutive equation. Constitutive equations cover those applied to both metallic and non-metallic materials. Some practical results were obtained for a particular form of a hypoelastic equation which resembles the Drucker-Prager criterion for the form of the limit state. Results were also examined against a set of experimental data.

Keywords

References

[1] Oliver, J., Cervera, M., & Manzoli, O. (1999). Strong discontinuities and continuum plasticity models: the strong discontinuity approach. International Journal of Plasticity, 15(3), 319-351. https://doi.org/10.1016/S0749-6419(98)00073-4
[2] Holtz, R. D., Kovacs, W. D., & Sheahan, T. C. (1981). An introduction to geotechnical engineering (Vol. 733). Englewood Cliffs: Prentice-Hall.
[3] Mohr, O. (1900). Welche umstände bedingen die elastizitätsgrenze und den bruch eines materials. Zeitschrift des Vereins Deutscher Ingenieure, 46(1524-1530), 1572-1577.
[4] Sulem, J., & Vardoulakis, I. G. (1995). Bifurcation analysis in geomechanics. CRC Press.
[5] Atkinson, J. H., & Bransby, P. L. (1977). The mechanics of soils: an introduction to critical state soil mechanics. McGraw-Hill Book Company.
[6] Johnson, W., Sowerby, R., Venter, R. D., & Kobayashi, S. (1983). Plane-strain slip-line fields for metal-deformation processes. Journal of Applied Mechanics, 50(3), 702. https://doi.org/10.1115/1.3167124
[7] Chen, W. F., & Liu, X. L. (2012). Limit analysis in soil mechanics. Elsevier.
[8] Truesdell, C. (1955). Hypo-elasticity. Journal of Rational Mechanics and Analysis, 4, 83-1020. https://www.jstor.org/stable/24900356
[9] Noll, W. (1955). On the continuity of the solid and fluid states. Journal of Rational Mechanics and Analysis, 4, 3-81. https://doi.org/10.1512/IUMJ.1955.4.54001
[10] Tokuoka, T. (1971). Yield conditions and flow rules derived from hypo-elasticity. Archive for Rational Mechanics and Analysis, 42, 239-252. https://doi.org/10.1007/BF00282332
[11] Drǎguşin, L. (1998). Bifurcations in the mechanics of hypoelastic composite materials. International Journal of Engineering Science, 36(15), 1839-1862.
https://doi.org/10.1016/S0020-7225(98)00011-1
[12] Careglio, C., Canales, C., García Garino, C., Mirasso, A., & Ponthot, J. P. (2016). A numerical study of hypoelastic and hyperelastic large strain viscoplastic Perzyna type models. Acta Mechanica, 227, 3177-3190. https://doi.org/10.1007/s00707-015-1545-6
[13] Lourenco, J. C., dos Santos, J. A., & Pinto, P. (2017). Hypoelastic UR-free model for soils under cyclic loading. Soil Dynamics and Earthquake Engineering, 97, 413-423. https://doi.org/10.1016/j.soildyn.2017.03.009
[14] Challamel, N., Nicot, F., Wautier, A., Darve, F., & Lerbet, J. (2022). Hyperelastic or hypoelastic granular circular chain instability in a geometrically exact framework. Journal of Engineering Mechanics, 148(9), 04022053. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002139
[15] Veiskarami, M., Azar, E., & Habibagahi, G. (2023). A rational hypoplastic constitutive equation for anisotropic granular materials incorporating the microstructure tensor. Acta Geotechnica, 18(3), 1233-1253. https://doi.org/10.1007/s11440-022-01661-y
[16] Shirazizadeh, S., Veiskarami, M., & Ghabezloo, S. (2023). A Study on the initiation of discontinuities in hypoplastic granular materials for some simple motion fields in classical continua. Journal of Engineering Mechanics, 149(1), 04022093.
https://doi.org/10.1061/(ASCE)EM.1943-7889.0002173
[17] Romano, M. (1974). A continuum theory for granular media with a critical state. Polish Scientific Publishers IFTR.
[18] Mašín, D., & Mašín, D. (2019). Tensorial hypoplastic models. Modelling of Soil Behaviour with Hypoplasticity: Another Approach to Soil Constitutive Modelling, 73-85. https://doi.org/10.1007/978-3-030-03976-9_4
[19] Yang, Z., Liao, D., & Xu, T. (2020). A hypoplastic model for granular soils incorporating anisotropic critical state theory. International Journal for Numerical and Analytical Methods in Geomechanics, 44(6), 723-748. https://doi.org/10.1002/nag.3025
[20] Amiri, M., & Ebrahimi, R. (2019). Simulation of a new process design to fabricate a rectangular twist waveguide using extrusion and a twist die. Iranian Journal of Materials Forming, 6(2), 52-61. https://doi.org/10.22099/IJMF.2019.5439
[21] Truesdell, C. (1965). The non-linear field theories of mechanocs. Encyclopedia of Physics, 3, 5-8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46015-9_1
[22] Kolymbas, D., & Herle, I. (2003). Shear and objective stress rates in hypoplasticity. International Journal for Numerical and Analytical Methods in Geomechanics, 27(9), 733-744.
https://doi.org/10.1002/nag.297
[23] Russell, A. R., & Khalili, N. (2004). A bounding surface plasticity model for sands exhibiting particle crushing. Canadian Geotechnical Journal, 41(6), 1179-1192. https://doi.org/10.1139/T04-065
 
Iranian Journal of Materials Forming
Volume 11, Issue 1
January 2024
Pages 34-43

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