THE HOMOGENIZATION OF VISCOELASTIC TRANSTROPIC COMPOSITE MATERIAL

  • A. V. Gatsenko Zaporizhzhia National University
  • M. I. Klymenko Zaporizhzhia National University
  • M. O. Korzyukov Zaporizhzhia National University
  • N. O. Dioba Zaporizhzhia National University
Keywords: composite material, matrix, fiber, longitudinal tension, longitudinal shear, effective characteristic, energy criterion

Abstract

The paper proposes a method for determining the parameters of integral operators for the effective characteristics of a composite material. It is assumed that the fibrous composite is viscoelastic and transversely isotropic. The fibers in the matrix are oriented in one direction. The fiber and matrix are transversely isotropic, the fiber is perfectly elastic, and the matrix is viscoelastic. The isotropy planes of the matrix and fiber coincide and are perpendicular to the fiber axis. The representative element of the composite is a cylindrical cell. It consists of two coaxial cylinders. The fiber is a solid cylinder, the matrix is hollow. In the considered model, the Poisson's ratios of the viscoelastic material are assumed to be constant, the longitudinal elastic modulus of the first kind and the longitudinal shear modulus are defined as integral operators. The characteristics of the operators of the longitudinal elastic modulus of the first kind and the longitudinal shear modulus are determined. The mechanical behavior is determined after solving following problems 1) joint elastic deformation of the matrix and the fiber; 2) modelling of homogeneous composite. The axisymmetric stress-strain state of the matrix, fiber, and homogeneous composite is considered. For longitudinal tension, it is assumed that the axial displacements of the matrix and fiber coincide, the radial displacements and stresses at the interface of the matrix and the fibers are continuous, and there are no stresses at the cell boundary. For the longitudinal shear at the interface between the matrix and the fiber, the tangential stresses and axial displacements coincide, and the harmonic tangential stress is specified on the outer surface of the composite. For each boundary value problem, stresses, displacements, and deformations are determined. This makes it possible to determine for each case the energy of elastic volumetric deformation of the matrix, fiber, and homogeneous composite. An energy criterion is applied to determine the effective constants of an elastic composite. It consists in the fact that the energy of elastic bulk deformation of a homogeneous composite is equal to the sum of the values of such energies for the matrix and fiber. The solution of this problem in the viscoelastic case is obtained as elastic solution of the problem of composite homogenization. The rheological characteristics of the matrix and the homogeneous composite are determined by the relations of the hereditary Boltzmann-Volterra theory. The viscoelastic characteristics of the material are modeled by convolution-type integral equations. This allows to apply the Laplace transform.

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Published
2020-03-02
How to Cite
Gatsenko, A. V., Klymenko, M. I., Korzyukov, M. O., & Dioba, N. O. (2020). THE HOMOGENIZATION OF VISCOELASTIC TRANSTROPIC COMPOSITE MATERIAL. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences, (2), 21-28. Retrieved from http://journalsofznu.zp.ua/index.php/phys-math/article/view/220