Keywords: stochastic composites, effective properties, nonlinear deformation.

One of the important problems of mechanics of composite materials is the investigation of stresses under elevated loads. Such a loading is associated with accumulation of damage what finally leads to fracture of material. Corresponding experimental date are reported in [1]. It is also important to have a theoretical characterization of microdeformations of the material. Then one can predict macrostresses in the material studied. A survey of theoretical papers dealing with microcracked elastic materials is presented in the paper [2]. A study of materials weakened by periodically or randomly distributed microcracks was performed in the papers [3,4] by using homogenization methods. In the papers [5,6,7] a stochastic model of microfracture of composite material was proposed. Moreover, an algorithm enabling the determination of nonlinear effective characteristics of layered composites with fibres was elaborated. Both the layers and fibres are assumed to be isotropic. Nonlinear behaviour of porous anisotropic materials was examined in the papers [8,9].

The aim of the present paper is to extend this approach to the case of porous composites with ellipsoidal inclusions. Both the porous matrix and inclusions are transversally isotropic. It is assumed that the matrix or inclusions are porous and the loading processes leads to the accumulation of damage in them. Fractured microvolumes are modelled by a system of randomly distributed quasispherical pores. The porosity balance equation and ratios determinig the effective elastic moduli for the case of transversally isotropic components are considered as basic relations. The effective moduli of such a material are determined using the stochastic equations of elasticity theory and the method of conditional moment functions [10]. Afterwards, on the basis of the combined iterative method and an algorithm enabling the calculation of nonlinear elastic characteristics of the composite considered was elaborated. The fracture criterion is assumed to be given by the limit value of intensity of average shear stresses occurring in the undamaged part of the material. Moreover, it is assumed that the yield strength is the random function of coordinates. The distribution of the functions is given by power-exponential formula.

The developed approach is realized with the help of the computational complex including modern personal computers. As an example, we shall construct the nonlinear diagrams of macro-deformation and research the behaviour of a transversally-isotropic porous material for biaxial expansion. The results of numerical calculations are presented in the form of figures which depict the dependence of macrostresses on macrodeformations for various factors such as porosity, volume concentration of phases and parameters of material strength scatter.

1

V.S. Kuksenko, V.P. Tamuzh, "Fracture micromechanics of polymer materials", [in Russian], Zinatne, Riga, 1978.

2

M. Kachanov, "Effective elastic properties of cracked solids: critical review of some basic concepts", Appl. Mech. Rev., 145(8), 304-335, 1992. doi:10.1115/1.3119761

3

B. Gambin, J.J. Telega, "Effective properties of elastic solids with randomly distributed microcracks", Mechanics Research Communications, 27(6), 697-706, 2000. doi:10.1016/S0093-6413(00)00143-9

4

J.J. Telega, "Homogenisation of fissured elastic solids in the presence of unilateral conditions and friction", Computational Mechanics, 6, 109-127, 1990. doi:10.1007/BF00350517

5

L.P. Khoroshun, "Principles of the micromechanics of material damage. 1. Short-term damage", International Applied Mechanics, 35(4), 1035-1041, 1998. doi:10.1007/BF02701060

6

L.P. Khoroshun, E.N. Shikula, "Deformation of composite material for microdestruction", International Applied Mechanics, 32(6), 52-58, 1996. doi:10.1007/BF02088412

7

L.P. Khoroshun, E.N. Shikula,, "Effect of the spread of strength characteristics of the binder on the deformation of laminar fibrous composite", International Applied Mechanics, 34(7), 39-45, 1998.

8

L.B. Nazarenko, "The influence of the microdestruction on the deformative properties of anisotropic materials", [in Russian], Dopovidy NAS of Ukraine, 10, 63-67, 1999.

9

L.P. Khoroshun, L.B. Nazarenko, "Model of Short-term Damaging of Transversally Isotropic Materials", International Applied Mechanics, 37(1), 74-83, 2001. doi:10.1023/A:1011312230221

10

L.P. Khoroshun, B.P. Maslov, E.N. Shikula, L.B. Nazarenko, "Statistical mechanics and effective properties of materials", [in Russian], Naukova Dumka, Kiev, 1993.

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