Analytical solution of physically nonlinear problem for an inhomogeneous thick-walled cylindrical shell

Among the classical works devoted to Solid Mechanics a significant place is occupied by the studies taking into account the physical and geometric nonlinearity. Also there is enough of works, which concern linear problems taking into account the inhomogeneity of the material. At the same time there are very few publications, which take into account both effects (non-linearity and inhomogeneity). This is due to the lack of experimental data on the influence of various factors on the parameters defining the non-linear behavior of the materials. Thus it is of great importance to study the influence of inhomogeneity when solving the problems of structures made of physically nonlinear materials. This article provides a solution to one of the problems of the nonlinear theory of elasticity taking into account the inhomogeneity. The problem is solved in an axisymmetric formulation, i.e. all the parameters of the nonlinear relationship between the intensities of stresses and strains are functions of the radius. The article considers an example - the stress distribution in the inhomogeneous soil massif with a cylindrical cavity.

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MODEL OF DEFORMATION OF FIBROUS MATERIALS OF MULTIDIRECTIONAL REINFORCEMENT WITH NONORIENTED FIBERS

Collection of scientific works of the State University of Infrastructure and Technologies series Transport Systems and Technologies ◽

10.32703/2617-9040-2021-37-12 ◽

2021 ◽

Vol 1 (37) ◽

pp. 119-129

Author(s):

E. Shikula

Keyword(s):

Strain State ◽

Fibrous Composite ◽

Theory Of Elasticity ◽

Fibrous Materials ◽

Thermoelastic Properties ◽

Fibrous Composite Material ◽

Conditional Moments ◽

Second Stage ◽

Two Stages ◽

Nonlinear Theory Of Elasticity

A model of deformation of multidirectional reinforcement fibrous materials with differently oriented fibers is proposed. The solution to the problem is built in two stages. At the first stage, the known properties of fibers and binder are used to determine the effective thermoelastic properties and stress-strain state of the subsystem with fibers oriented in a certain way relative to the main coordinate system. It is based on stochastic differential equations of the physically nonlinear theory of elasticity using the method of conditional moments. At the second stage, using a given distribution function based on the Voigt scheme, a model of deformation of the entire system is constructed from the calculated properties of the subsystems. Strain curves are obtained for simple loading, and the deformation of materials at uniform orientation of fibers is investigated. It was found that a fibrous composite material with differently oriented fibers in a macrovolume is isotropic, and its effective thermoelastic constants substantially depend on the volumetric content of fibers.

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Ut vis sic tensio

Theoretical and Applied Mechanics ◽

10.2298/tam170703011s ◽

2018 ◽

Vol 45 (1) ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Giuseppe Saccomandi

Keyword(s):

Experimental Data ◽

Mechanical Properties ◽

Elastic Strain ◽

Strain Energy ◽

Nonlinear Response ◽

Solid Mechanics ◽

Functional Form ◽

Elastic Strain Energy ◽

Strongly Nonlinear ◽

Long Time

The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

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