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<p>The stress state of a&#xa0;transverse rectangular plastic layer in a&#xa0;stretchable heterogeneous plastic strip under plane deformation at a&#xa0;critical moment of loading is studied. The layer consists of a&#xa0;less durable material than the rest of the strip, and the strength parameter at the contact boundary has a&#xa0;jump. The material of the strip, including the layer, is heterogeneous. The strength parameter is determined by the inhomogeneity function, which depends on the distance to the longitudinal axis of symmetry of the strip. As a&#xa0;simplifying condition, it is assumed that the tangential stresses in some neighborhood of the longitudinal axis of symmetry depend linearly on the distance to it. The nature of the distribution of normal stresses at the contact boundary is investigated. Explicit analytical expressions are obtained for the approximate calculation of stresses in the plastic layer and the critical load for some special cases of the heterogeneity function.</p>

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On an analytical model of the critical state of an heterogeneous plastic layer: a closed-form solution for a special case

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Valerii L. Dilman,
  • Alexandra E. Kashcheeva

摘要

The stress state of a transverse rectangular plastic layer in a stretchable heterogeneous plastic strip under plane deformation at a critical moment of loading is studied. The layer consists of a less durable material than the rest of the strip, and the strength parameter at the contact boundary has a jump. The material of the strip, including the layer, is heterogeneous. The strength parameter is determined by the inhomogeneity function, which depends on the distance to the longitudinal axis of symmetry of the strip. As a simplifying condition, it is assumed that the tangential stresses in some neighborhood of the longitudinal axis of symmetry depend linearly on the distance to it. The nature of the distribution of normal stresses at the contact boundary is investigated. Explicit analytical expressions are obtained for the approximate calculation of stresses in the plastic layer and the critical load for some special cases of the heterogeneity function.