Determination of Effective Characteristics of a Fibrous Composite with Account of Viscoelastic Deformation of its Compon
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SCIENTIFIC AND TECHNICAL SECTION DETERMINATION OF EFFECTIVE CHARACTERISTICS OF A FIBROUS COMPOSITE WITH ACCOUNT OF VISCOELASTIC DEFORMATION OF ITS COMPONENTS À. F. Bulat,a V. I. Dyrda,a,1 S. M. Grebenyuk,b and M. I. Klymenko
UDC 539.3
b
A technique for determination of viscoelastic characteristics of transversal-isotropic fiber composite with isotropic components – viscoelastic matrix and elastic fiber – is proposed. The compositeunity cell consisting of two infinite coaxial cylinders is investigated by the representative element method. The solid and hollow cylinders are used to simulate the fiber and matrix, respectively. Characteristics of isotropic components of the composite are expressed through the bulk and shear moduli. The viscoelastic properties of the matrix and the homogenized composite are modeled by integral ratios of the hereditary Volterra theory. The Laplace transform is used to find the components of the axisymmetric stress-strain state of the cell and its components under uniform longitudinal tension. This make it possible to replace integral operators by algebraic functions. The effective rheological characteristics of a transversal-isotropic viscoelastic composite are determined by fitting displacements of a representative element of the viscoelastic composite and its components. Keywords: composite, fiber, matrix, bulk strain modulus, shear modulus, integral operator, viscoelasticity, effective characteristics, instantaneous elastic modulus, relaxation core. Introduction. The development of modern technology is closely related to the use of composite materials. The use of composites allows optimizing technical and economic characteristics of products. Therefore, design of constructions in modern engineering involves preliminary modeling of mechanical properties of composite materials, which in many cases are viscoelastic. The task of homogenization of the viscoelastic composite is important, i.e., to present it as a homogeneous material whose rheological functions need to be determined. Unidirectional fibrous composites are widely used in engineering and construction, they show viscoelastic and anisotropic properties. That is why the researches on development of homogenization methods, which allow to determine similar characteristics of the composite by known mechanical characteristics of matrix and fiber, are relevant. Research Analysis. Many studies have been devoted to the problem of homogenization of fiber composites. An example of numerous homogenization of a unidirectional fiber composite using the finite element method using the ANSYS software package is study [1]. In [2], on the example of unidirectional epoxy carbon-fiber composite and laminates, the most common methods of homogenization of fibrous composites are evaluated, and the results obtained are compared with experimental ones. Analytical and numerical methods for solving viscoelasticity problems of heterogeneous and anisotropic materials, including composites, are described in detail. The main mathematical models of viscoel
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