APPLICATION OF THE METHOD OF CONDITIONAL MOMENTS TO INVESTIGATING THE DEFORMATION PROPERTIES OF ORTHOTROPIC COMPOSITES WITH FIBER MICRODAMAGES L. Nazarenko,* ** L. P. Khoroshun,* W. H. Müller,** and B. R. Wille** Keywords: orthotropic composite material, stochastic structure, microdamages, porosity, effective character- istics, Weibull distribution, porosity balance equation A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical pores. The porosity balance equation and relations for de- termining the effective elastic moduli for the case of a fibrous composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random function of coordi- nates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algo- rithm for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams for an orthotropic composite in uniaxial tension are obtained. 1. Introduction. The problem of deformation of composite materials operating under rather high loads is of great theoretical and practi- cal interest. Experimental investigations of the stress-strain state of composite materials are complicated and expensive; in this connection, there arises the necessity for elaborating new investigation methods to establish a connection between the deformability and strength of such a material and its physicomechanical characteristics. In real materials, the microstrength is nonuniform, i.e., microdamages arise only in some part of their “weak” microvolumes under a load, while the other part does not fail [1-4]. The accumulation of scattered damages decreases the effective (load-carrying) cross-sectional area and leads to a redistribution of stresses. Due to the appearance of additional porosity, the stiffness of the material decreases, and relations be- tween the macrostresses and macrostrains become nonlinear. In statistical approaches, it is assumed that the microstrength of a 11 0191-5665/09/4501-0011 © 2009 Springer Science+Business Media, Inc. *Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine. **Institute of Mechanics, Techni- cal University, Berlin, Germany. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17-30, Janu- ary-February, 2009. Original article submitted September 25, 2008. Mechanics of Composite Materials, Vol. 45, No. 1, 2009