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Modeling of Plastic Deformation Based on the Theory of an Orthotropic Cosserat Continuum

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Abstract

In the paper, the plastic deformation of heterogeneous materials is analyzed by direct numerical simulation based on the theory of an elastic-plastic orthotropic Cosserat continuum, with the plasticity condition taking into account both the shear and rotational mode of irreversible deformation. With the assumption of a block structure of a material with elastic blocks interacting through compliant plastic interlayers, this condition imposes constraints on the shear components of the asymmetric stress tensor, which characterize shear, and on the couple stresses, which irreversibly change the curvature characteristics of the deformed state of the continuum upon reaching critical values. The equations of translational and rotational motion together with the governing equations of the model are formulated as a variational inequality, which correctly describes both the state of elastic-plastic deformation under applied load and the state of elastic unloading. The numerical implementation of the mathematical model is performed using a parallel computing algorithm and an original software for cluster multiprocessor systems. The developed approach is applied to solve the problem of compressing a rectangular brick-patterned blocky rock mass by a rough nondeformable plate rotating with constant acceleration. The effect of the yield stress of the compliant interlayers on the stress-strain state of the rock mass in shear and bending is studied. The field of plastic energy dissipation in the rock mass is analyzed along with the fields of displacements, stresses, couple stresses, and rotation angle of structural elements. The obtained results can help to validate the hypothesis about the predominant effect of curvature on plastic strain localization at the mesolevel in microstructural materials.

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Funding

The work was carried out at the financial support of Beijing High-Caliber Talent from Overseas (BHT0 201612129-WD). It was also supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2020-1631).

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Authors and Affiliations

  1. Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences , 660036, Krasnoyarsk, Russia

    V. M. Sadovskii & O. V. Sadovskaya

  2. Siberian Federal University , 660041, Krasnoyarsk, Russia

    V. M. Sadovskii

  3. Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences , 690041, Vladivostok, Russia

    M. A. Guzev

  4. Beijing University of Civil Engineering and Architecture , 100044, Beijing, China

    M. A. Guzev & Ch. Qi

Authors
  1. V. M. Sadovskii
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  2. M. A. Guzev
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  3. O. V. Sadovskaya
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  4. Ch. Qi
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Correspondence to V. M. Sadovskii.

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Russian Text © The Author(s), 2019, published in Fizicheskaya Mezomekhanika, 2019, Vol. 22, No. 2, pp. 59–66.

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Sadovskii, V.M., Guzev, M.A., Sadovskaya, O.V. et al. Modeling of Plastic Deformation Based on the Theory of an Orthotropic Cosserat Continuum. Phys Mesomech 23, 223–230 (2020). https://doi.org/10.1134/S1029959920030066

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