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Abstract <p>In accordance with Volterra’s linear theory, applicable to a wide range of materials with amorphous and heterogeneous structures, integral type operators are present in the defining relationships that determine the behavior of continuous media with the memory of the medium. In the initial boundary value problem for these equations, the kernel of the integral operator is represented as a weakly singular kernel (the Rabotnov function). To perform numerical calculations in applied problems, it is necessary to know the elastic and viscous constants describing the behavior of the material. In the current work, analysis methods and the Nelder-Mead algorithm (simplex method) from optimization theory are used to determine these parameters in determining ratios.</p>

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Determination of Parameters of Integral Operators for the Initial Boundary Value Problem of the Theory of Viscoelasticity on Creep Curves

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • D. A. Prikazchikov,
  • I. B. Petrov

摘要

Abstract

In accordance with Volterra’s linear theory, applicable to a wide range of materials with amorphous and heterogeneous structures, integral type operators are present in the defining relationships that determine the behavior of continuous media with the memory of the medium. In the initial boundary value problem for these equations, the kernel of the integral operator is represented as a weakly singular kernel (the Rabotnov function). To perform numerical calculations in applied problems, it is necessary to know the elastic and viscous constants describing the behavior of the material. In the current work, analysis methods and the Nelder-Mead algorithm (simplex method) from optimization theory are used to determine these parameters in determining ratios.