Model of deformation of in-plane reinforced fiberous materials with physically nonlinear matrix
DOI:
https://doi.org/10.17721/1812-5409.2026/1.22Keywords:
fibrous composite material, in-plane reinforced materials, nonlinear matrix, effective deformation properties, stress-strain state, influence of nonlinearity, computer modelingAbstract
With increasing load, many homogeneous and composite materials exhibit nonlinear relationships between macrostresses and macrostrains. This may be due to the physical nonlinearity of component deformation. Fibrous materials are used in structures and parts operating under high force and temperature loads. Therefore, predicting their nonlinear properties is relevant.
The aim of the work is to build a model and study the nonlinear deformation of in-plane reinforced fibrous composite materials with a physically nonlinear matrix.
In-plane reinforced fibrous materials are considered as multicomponent materials with a random arrangement of fibers, considering the matrix and fibers of each direction as separate components. We will assume that the fiber material is transversely isotropic with an axis of symmetry along the fibers, the matrix material is isotropic physically nonlinear. The determination of the effective deformation properties and the stress-strain state of the material is carried out in two stages. At the first stage, the properties of the subsystem, which is a unidirectional fibrous material formed by fibers of a certain direction and part of the matrix, are determined. The solution of the first stage problem is carried out on the basis of a model of a unidirectional fibrous material of a stochastic structure. The solution is built using the method of conditional moments of L.P. Khoroshun. At the second stage, the effective properties of the entire system are determined based on the calculated properties of the subsystems. The solution is built on the basis of the Voichta scheme. Nonlinear equations that take into account the physical nonlinearity of the matrix are solved by the iterative method.
An algorithm for determining the effective properties and stress-strain state of a material with a physically nonlinear matrix has been developed. The laws of the relationship between macrostresses and macrostrains in the material and the dependence of the average strains and stresses in the material matrix on macrostrains have been established. The deformation curves of the material have been studied. It has been established that the nonlinearity of the components significantly affects the effective deformation properties and the stress-strain state of the material.
Pages of the article in the issue: 165 - 169
Language of the article: Ukrainian
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Copyright (c) 2026 Elena Shikula, Nataliia Zhukova, Victor Vyshnivskyi, Svitlana Bilousova
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