SOME DEVELOPMENTS FOR MATHEMATICAL THEORY OF MODERN MECHANICS

Zhuravkov M.A., Doctor of Physical and Mathematical Sciences, Professor, Vice-Rector, Head of the Department "Theoretical and applied mechanics", Belarusian State University, Minsk, Republic of Belarus

Pleskachevsky Yu.M., Corresponding Member of the NAS of Belarus, Doctor of Technical Sciences, Professor, Chairman of the Presidium of the Gomel branch of the NAS of Belarus, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

Romanova N.S., Head of the Department of Youth Programs and Projects, Competitor of the Department of Theoretical and Applied Mechanics, Mechanical and Mathematical Faculty of the Belarusian State University, Minsk, Republic of Belarus

Classical development and the formation of some new modern branches in mechanics require continuous improvement and modification of mathematical models and methods to solve the model problems. In this article we consider some developments in mechanics and mathematical models for the description of the mechanical state and different material behaviour and perspectives of fractional calculus for the use in mechanics, and describe the conjugate biophysical and biomechanical problems, the mathematical models of material deformation taking into account their complex heterogeneous structure.

mechanical and mathematical models of fractional order, generalized model of Maxwell, Kelvin-Voigt, Zener, models of viscoelasticity, heterogeneous environments

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