A stochastic model for behavior analysis of fiber-reinforced quasi-brittle materials

Short fiber reinforced composites are established as a class of materials today. Modeling of such heterogeneous materials is still in the development stage. A proposed model which combines stochastic concepts with micromechanical approach is designed to predict the behavior of such materials. It is based on stochastic models for material behavior and combines the classical theory of deformation with a statistical treatment of imperfect materials. The model uses the principle of superposition of strain rates as a basis. Therefore such deformations as microcracking, plastic flow, thermoelastic behavior, and growth, coalescence and nucleation of voids, and crack-fiber interaction as well as most other kinds of inelastic behavior can be incorporated in the model. The stochastic material theory is expanded to predict a variety of uncertain material behavior. In the new model, such characteristics as random positions of fibers in the matrix, interactions between random cracks and fibers, change in the overall material behavior due to the changes in the structure of fibers and cracks during a loading process, deformation due to microcracking are treated by analyzing the 'open' and 'closed' cracks and considering the shearing of closed cracks. In this model, cracks are assumed to be circular (penny-shaped), and of random orientations and size, described by a probability density function. Available analytical solutions for the opening cracks and for the stability of penny-shaped cracks (both for tension and shear) are combined and included in the model to account for any arbitrary state of stress. Plastic flow is characterized by a kinematic-hardening model; and large deformations are accounted for through the polar decomposition theorem by separating them each into a stretch and a rotation component. Distinction between the fixed and rotating reference frames (which is crucial for isotropic materials) is also made; and elastic modulus is taken as a variable to account for the microcracking behavior.