Solution of one boundary value task of viscoelasticity in a nonlinear formulation, in the case of a cubic stress-strain relation

Authors

  • B.D. Dzhanmuldaev Korkytata Kyzylorda University, Kyzylorda, Kazakhstan
  • A. Janmuldaeva Eurasian National University, Astana, Kazakhstan
  • Zh. Jalbyrova Korkytata Kyzylorda University, Kyzylorda, Kazakhstan
  • A.K Smakhanova Korkytata Kyzylorda University, Kyzylorda, Kazakhstan
  • A.Z. Madelkhanova Korkytata Kyzylorda University, Kyzylorda, Kazakhstan

DOI:

https://doi.org/10.26577/ijmph.2023.v14.i2.02
        201 188

Abstract

In this paper, the solution of a boundary value task in the nonlinear formulation is considered by the authors [1][2]. In spite of its proximity to linear theory, the nonlinear theory of viscoelasticity has not yet been fully developed. This issue is far from being fully completed, since the existing calculation methods do not yet provide a complete answer to the many different questions posed by  practice.   For  this  reason,  in  order  to  obtain  a  nonlinear  law  relating  the  strains  σij  and deformations εij a number of conditions are formed:

  • The specific work of deformation A must be a function of the entire deformation history from the beginning of deformation to the current time
  • The material of a viscoelastic body is homogeneous and
  • For very  small  deformations  the  nonlinear  relation  law  between  σij  and  εij  in  the  limit should pass to relations in linear

 

 

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Published

2023-12-29

How to Cite

Dzhanmuldaev, B. ., Janmuldaeva, A., Jalbyrova, Z., Smakhanova, A., & Madelkhanova, A. . (2023). Solution of one boundary value task of viscoelasticity in a nonlinear formulation, in the case of a cubic stress-strain relation. International Journal of Mathematics and Physics, 14(2), 17–24. https://doi.org/10.26577/ijmph.2023.v14.i2.02