Abstract:
Nowadays, polymers are widely used in various fields. Such materials often exhibit viscoelastic properties. Engineering analysis considering viscoelasticity is laborious and requires certain expertize. This paper proposes a method for solving linear viscoelastic
problems in a simpler way and presents a variant of the solution extension to an anisotropic case.
The Volterra correspondence principle allows one to analyze viscoelastic bodies on the
basis of the analytical solution like an elastic problem. The developed method is described in a similar way. It allows determining of some functions of time and material
constants whose values at a certain point in time can be used as elastic constants. The solutions to these two problems are identical. To substantiate this statement, the authors
consider the conditions for maximum equivalence of specific potential energy functionals
of strain and stress (for the cases of kinematic and force boundary conditions, respectively)
of viscoelastic and reference elastic media. The functions satisfying these conditions
have been found, and a new method for solving the problems of linear viscoelasticity of
an anisotropic body has been shown using several examples.
Keywords:effective modules of Lagrange and Castilian types, variational problem, anisotropy, orthotropy, integral operators.
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