Principle of the overlay deformations in the theory of creep

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Abstract

The aim of the research is to justify in the non-linear statement the overlay principle of fraction creep deformation, known in the linear creep theory as Bolzmann’s principle of superposition. Methods. In contrast to the traditional approach the material of constructive elements is considered as an union of its links with statistical disturbed strength. The model of structural strength allows the deduction of rheological equations. In loading process so called structural stresses of capable to resist links are considered. Results. The modification Bolzmann’s principle of superposition for fraction creep deformations is proposed. This permits its applicability also under non-linearly dependence of deformations on stresses. In according to concept of the statistical distribution of the strengths of links and linear dependence of determinations on structural stresses the rheological of mechanical statement is reduced. This equation implies the suitable on relation problems the linear integral equation. The relation of structural strength of material with its energy of entirety and with the experimentally known independency of specific to strength deformation on age of concrete is showed. The correct interpretations of certain known mechanical state equations for concrete are represented.

About the authors

Evgeniy A. Larionov

Moscow State University of Civil Engineering

Author for correspondence.
Email: i.v.ivn@mail.ru

Doctor of Science (Technical), Professor of Department of Applied Mathematics

26 Yaroslavskoye Shosse, Moscow, 129337, Russian Federation

Vladimir I. Rimshin

Moscow State University of Civil Engineering

Email: i.v.ivn@mail.ru

Doctor of Science (Technical), Professor of Department of Construction; Corresponding Member of the Russian Academy of Architecture and Construction Sciences

26 Yaroslavskoye Shosse, Moscow, 129337, Russian Federation

Tatyana V. Zhdanova

Moscow State University of Civil Engineering

Email: i.v.ivn@mail.ru

graduate student of Department of Applied Mathematics

26 Yaroslavskoye Shosse, Moscow, 129337, Russian Federation

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Copyright (c) 2019 Larionov E.A., Rimshin V.I., Zhdanova T.V.

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