Mechanics of Deformable Solids
DOI: http://www.dx.doi.org/10.24866/2227-6858/2020-2-1

Guzev M., Gorbunov A.

MIKHAIL GUZEV, Academician of RAS, Professor, Director, e-mail: guzev@iam.dvo.ru
ANTON GORBUNOV, Employee of the Laboratory of Computational Informatics (Student, School of Natural Sciences, Far Eastern Federal University), e-mail: gorbunov.avia@students.dvfu.ru
Institute of Applied Mathematics, FEB RAS
Vladivostok, Russia

Non-Euclidean model of a continuous medium
and description of residual stresses

Abstract: Within the framework of the non-Euclidean model of a continuous medium for which the Saint-Venant compatibility condition for deformations is not fulfilled, an equation for the stress function is obtained. A representation is built for the field of internal stresses and it is shown to consist of the classic field of elastic stresses and the stress field parameterized through the incompatibility function. The non-Euclidean continuum model is used to describe the internal residual stresses in the samples. The phenomenological parameters of the model are determined on the basis of experimental data on the measurement of residual stresses.
Keywords: self-balanced stresses, residual stress, incompatibility, non-Euclidean model, plane-deformed state.

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