Abstract
Many structural materials, which are preferred for the developing of advanced constructions, are inhomogeneous ones. These materials have complex internal structure and properties, which make them to be more effectual in the solution of special problems required for development engineering. On the other hand, in consequence of this internal heterogeneity, they exhibit complex mechanical properties. In this work, the analysis of some features of the behavior of composite materials under different loading conditions is carried out. The dependence of nonlinear elastic response of composite materials on loading conditions is studied. Several approaches to model elastic nonlinearity such as different stiffness for particular type of loadings and nonlinear shear stress–strain relations are considered. Instead of a set of constant anisotropy coefficients, the anisotropy functions are introduced. Eventually, the combined constitutive relations are proposed to describe simultaneously two types of physical nonlinearities, one of which characterizes the nonlinearity of shear stress–strain dependency and another one determines the stress state susceptibility of material properties. The method for experimental determination of material’s functions is proposed. Quite satisfactory correlation between the theoretical dependencies and the results of experimental studies is demonstrated.
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References
Matzenmiller A, Lubliner J, Taylor RL (1995) A constitutive model for anisotropic damage in fiber-composites. Mech Mater 20:125–152
Puck A, Schürmann H (1998) Failure analysis of FRP laminates by means of physically based phenomenological models. Compos Sci Technol 58:1045–1067
Bogetti TA, Hoppel CPR, Harik VM, Newill JF, Burns BP (2004) Predicting the nonlinear response and progressive failure of composite laminates. Compos Sci Technol. doi:10.1016/S0266-3538(03)00217-3
Zinoviev PA, Grigoriev SV, Lebedeva OV, Tairova LP (1998) The strength of multilayered composites under a plane-stress state. Compos Sci Technol 58(7):1209–1223
Fedulov BN, Antonov FK, Safonov AA, Ushakov AE, Lomov SV (2014) Influence of fibre misalignment and voids on composite laminate strength. J Compos Mater. http://jcm.sagepub.com/content/early/2014/10/29/0021998314557533
Lubineau GA (2010) Pyramidal modeling scheme for laminates—identification of transverse cracking. Int J Damage Mech 19(4):499–518
Ladeveze P, Le Dantec E (1992) Damage modelling of the elementary ply for laminated composites. Compos Sci Technol 43:257–267
Smith EW, Pascoe KJ (1977) The role of shear deformation in the fatigue failure of a glass fiber-reinforced composite. Composites 8(4):237–243
Lagattu F, Lafarie-Frenot MC (2000) Variation of PEEK matrix crystallinity in APC-2 composite subjected to large shearing deformations. Compos Sci Technol 60:605–612
Makeev A, Ignatius C, He Y, Shonkwiler B (2009) A test method for assessment of shear properties of thick composites. J Compos Mater 43(25):3091–3105
Petit PH, Waddoups ME (1969) A method of predicting the nonlinear behavior of laminated composites. J Compos Mater 3(1):2–19
Schapery RA, Sun CT (2000) Time dependent and nonlinear effects in polymers and composites, Issue 1357. ASTM, Philadelphia
Chamis CC, Sinclar JH (1977) Ten-deg off-axis shear properties in fiber composites. Exp Mech 17:339–346
Hahn HT, Tsai SW (1973) Nonlinear elastic behavior of unidirectional composite laminae. J Compos Mater 7:102–118
Sims DF (1973) In-plane shear stress–strain response of unidirectional composite materials. J Compos Mater 7:124–128
Swanson SR, Messick M, Toombes GR (1985) Comparison of torsion tube and Iosipescu in-plane shear test results for a carbon fibre-reinforced epoxy composite. Composites 16(3):220–224
Sala G (2000) Mechanical characterization of angle–ply composite laminates by differential Moiré method: the influence of Specimens’ length-to-width ratio. Meccanica 35(5):421–432
He Y, Makeev A (2014) Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: a numerical study. Int J Solids Struct 51(6):1263–1273
Mantari JL, Bonilla EM, Guedes Soares C (2014) A new tangential-exponential higher order shear deformation theory for advanced composite plates. Compos B Eng 60:319–328
Weinberg M (1987) Shear testing of neat thermoplastic resins and their unidirectional graphite composites. Composites 18(5):386–392
Lomakin EV (2011) Constitutive models of mechanical behavior of media with stress state dependent material properties. Mechanics of generalized continua. Adv Struct Mater 7:339–350
Lomakin EV, Fedulov BN (2013) Plane strain extension of a strip made of a material with stress state type dependent material properties and weakened by cuts with circular base. Mech Solids 48(4):424–430
Lomakin EV, Rabotnov YuN (1978) A theory of elasticity for an isotropic body with different moduli in tension and compression. Mech Solids 13(6):25–30
Lomakin EV (2009) Plastic flow of dilatant solids with stress-state-dependent material properties. In: Gupta NK, Manzhirov AV (eds) Topical problems in solid mechanics. Elite Publishing House Pvt. Ltd., New Delhi, pp 122–132
Lomakin EV, Fedulov BN, Melnikov AM (2014) Constitutive models for anisotropic materials susceptible to loading conditions. In: Belyaev AK, Irschik H, Krommer M (eds) Mechanics and model-based control of advanced engineering systems. Springer, pp 209–216
Fedulov BN (2007) The limit plastic state of a holed strip made of a dilatant material. Moscow Univ Mech Bull 62(6):160–164
Alexandrov S, Jeng Y, Lomakin E (2014) An exact semi-analytic solution for residual stresses and strains within a thin hollow disc of pressure-sensitive material subject to thermal loading. Meccanica 49(4):775–794
Kratsch K, Schutzler J, Eitman D (1972) Carbon–carbon 3-D orthogonal material behavior. In: 13th Structures, structural dynamics and materials conference. AIAA paper, vol 72, 365 pp
Violeau D, Ladevèze P, Lubineau G (2009) Micromodel-based simulations for laminated composites. Compos Sci Technol 69:1364–1371
Lubineau G, Ladevèze P (2008) Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/Standard. Comput Mater Sci 43:137–145
deBotton G, Hariton I (2002) High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior. J Mech Phys Solids 50(12):2577–2595
Lenci S (2004) Elastic and damage longitudinal shear behavior of highly concentrated long fiber composites. Meccanica 39(5):415–439
Paggia M, Wriggers P (2012) Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces. J Mech Phys Solids 60(4):557–572
Talbot DRS (2000) Improved bounds for the effective properties of a nonlinear two-phase elastic composite. J Mech Phys Solids 48(6–7):1285–1294
Lekhnitskii SG (1963) Theory of the elasticity of an anisotropic elastic body. Holden Day, New York
Acknowledgments
This work was carried out in the Perm National Research Polytechnic University with support of the Government of Russian Federation (the Decree No. 220 on April 9, 2010) under the Contract No. 14.B25.310006, on June 24, 2013.
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Lomakin, E.V., Fedulov, B.N. Nonlinear anisotropic elasticity for laminate composites. Meccanica 50, 1527–1535 (2015). https://doi.org/10.1007/s11012-015-0104-5
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DOI: https://doi.org/10.1007/s11012-015-0104-5