Nonlinear elastic stress triaxiality dependent constitutive model for fibre-reinforced polymer composites

Nonlinear elastic stress triaxiality dependent constitutive model for fibre-reinforced polymer composites

OBID Štefan, HALILOVIČ Miroslav, STARMAN Bojan

Abstract. A novel constitutive model is proposed to describe fibre-reinforced polymer composite materials. The model covers three fundamental phenomena of such materials: anisotropy, tension-compression asymmetry, and nonlinear material behaviour. The model is based on the one-dimensional Ramberg-Osgood relation, which is extended to a multiaxial anisotropic form. Tension-compression asymmetry is then implemented with the introduction of stress triaxiality dependency. Finally, the model is verified using experimental data where the material response in uniaxial tension, uniaxial compression and shear stress states were measured.

Keywords
Constitutive Model, Stress Triaxiality Dependency, Anisotropic Material

Published online 4/19/2023, 10 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: OBID Štefan, HALILOVIČ Miroslav, STARMAN Bojan, Nonlinear elastic stress triaxiality dependent constitutive model for fibre-reinforced polymer composites, Materials Research Proceedings, Vol. 28, pp 1387-1396, 2023

DOI: https://doi.org/10.21741/9781644902479-150

The article was published as article 150 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] E.V. Lomakin, Y.N. Rabotnov, A theory of elasticity for an isotropic body with different moduli in tension and compression, Mech. Solid. 13 (1978) 25-30.
[2] Y. He, A. Makeev, Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study, Int. J. Solid. Struct. 51 (2014) 1263-1273. https://doi.org/10.1016/j.ijsolstr.2013.12.014
[3] S.A. Ambartsumian, A.A. Khachatrian, Basic equations in the theory of elasticity for materials with different resistance to tension and compression, Inzhenernyi zhurnal – Mekhanika tverdogo tela (1966) 44–53.
[4] R.M. Jones, Stress-strain relations for materials with different moduli in tension and compression, Aiaa J. 15 (1977) 16-23.
[5] C.W. Bert, Models for fibrous composites with different properties in tension and compression, J. Eng. Mater. Technol. 99 (1977) 344-349. https://doi.org/10.1115/1.3443550
[6] B.P. Patel, K. Khan, Y. Nath, A new constitutive model for bimodular laminated structures: Application to free vibrations of conical/cylindrical panels, Compos. Struct. 110 (2014) 183-191. https://doi.org/10.1016/j.compstruct.2013.11.008
[7] K. Vijayakumar, K.P. Rao, Stress-strain relations for composites with different stiffnesses in tension and compression, Comput. Mech. 2 (1987) 167-175. https://doi.org/10.1007/BF00571022
[8] L. Zhang, H.W. Zhang, J. Wu, B. Yan, A stabilised complementarity formulation for nonlinear analysis of 3D bimodular materials, Acta Mech. Sin. 32 (2016) 481-490. https://doi.org/10.1007/s10409-015-0517-3
[9] J. Park, J.W. Yoon, A general FRC (fiber reinforced composite) constitutive model considering transverse isotropy and accumulated damage, J. Mech. Sci. Tech. 36 (2022) 6147-6156. https://doi.org/10.1007/s12206-022-1129-z
[10] M. Latorre, F.J. Montáns, Bi-modulus materials consistent with a stored energy function: Theory and numerical implementation, Comput. Struct. 229 (2020) 106176. https://doi.org/10.1016/j.compstruc.2019.106176
[11] Z. Du, G. Zhang, T. Guo, S. Tang, X. Guo, Tension-compression asymmetry at finite strains: A theoretical model and exact solutions, J. Mech. Phys. Solid. 143 (2020) 104084. https://doi.org/10.1016/j.jmps.2020.104084
[12] E.V. Lomakin, B.N. Fedulov, Nonlinear anisotropic elasticity for laminate composites, Meccanica 50 (2015) 1527-1535. https://doi.org/10.1007/s11012-015-0104-5
[13] E.V. Lomakin, O.P. Shchendrigina, Stresses and strains in a disk of physically nonlinear material with stress state dependent properties, Mech. Solid. 55 (2020) 475-481. https://doi.org/10.3103/S0025654420040081
[14] W. Ramberg, W.R. Osgood, Description of stress-strain curves by three parameters, Technical Report NACA-TN-902, 1943.
[15] E.W. Smith, K.J. Pascoe, The role of shear deformation in the fatigue failure of a glass fibre-reinforced composite, Compos. 8 (1977) 237-243.