Solution of longitudinal shear problems of physically nonlinear bodies with properties depending on the type of stress state

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Deformation properties of structural materials, rocks, composite materials, etc. depend on the type of external action, and the degree of this dependence is determined by the structural features of the materials. These materials are characterized by a relationship between volume and shear deformation. Deformation curves are nonlinear even at small deformations. This paper presents constitutive relations describing the nonlinear behavior of these materials under small deformations. It is shown that classical hypotheses of anti-plane shear cannot be applied. The problem of anti-plane shear of a long prismatic body with a square cross-section containing a round through hole in the plane of the cross-section is solved numerically. It is shown that under shear loading conditions, the body is characterized by a triaxial stress state and a change in volume.

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Sobre autores

E. Lomakin

Lomonosov Moscow State University

Autor responsável pela correspondência
Email: evlomakin@yandex.ru

Corresponding Member of the RAS

Rússia, Moscow

O. Korolkova

Lomonosov Moscow State University; Research Institute of Mechanics of Lomonosov Moscow State University

Email: ol.shendrigina@mail.ru
Rússia, Moscow; Moscow

Bibliografia

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  2. Fedulov B.N., Bondarchuk D.A., Lomakin E.V. Longitudinal elastic nonlinearity of composite material // Frattura ed Integrità Strutturale. 2024. V. 18. № 67. P. 311–318. https://doi.org/10.3221/IGF-ESIS.67.22
  3. Obid Š., Halilovič M., Urevc J., Starman B. Non-linear elastic tension–compression asymmetric anisotropic model for fibre-reinforced composite materials // Intern. J. Engineering Science. 2023. V. 185. 103829. https://doi.org/10.1016/j.ijengsci.2023.103829
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  6. Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials Using a Combined Loading Compression (CLC) Test Fixture // ASTM International. 2016. ASTM D6641/D6641M-16e2. https://doi.org/10.1520/D6641_D6641M-16E01
  7. Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus // ASTM International. 2017. ASTM E111-17. https://doi.org/10.1520/E0111-17
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  13. Lomakin E., Korolkova O. Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear // Acta Mechanica 2024. V. 235. P. 6585–6597. https://doi.org/10.1007/s00707-024-04034-6
  14. Ramberg W., Osgood W.R. Description of stress-strain curves by three parameters: Technical Report NACA-TN-902. 1943.

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2. Fig. 1. Equivalent stress-strain curves for gray cast iron SCh 15–32 at different values of the parameter ξ: ⅓ (1), 0.232 (2), 0 (3), –0.064 (4), –0.126 (5), –⅓ (6).

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3. Fig. 2. Section of the body under consideration under longitudinal shear conditions.

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4. Fig. 3. Distribution of deformations (a) and stresses (b) along the straight line x₂ = 0.

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5. Fig. 4. Distribution of deformations (a) and stresses (b) along the straight line x₁ = 0.

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6. Fig. 5. Volumetric deformation (a) and hydrostatic pressure (b) at x₁² + x₂² = a²

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