The Problem of the Local Stress/strain Modes in the Matrix of Fibrous Composites

Abstract

On the basis of numerical solutions of the cellular problem of the theory of elasticity, an analysis was made of the deformation modes of the binder cross-reinforced with fibers of the composite at the microlevel. All possible types of local deformation of the binder of the fiber-reinforced composite, predicted in the simplified model in (Kalamkarov A L, Kolpakov A G: Analysis, Design and Optimization of Composite Structures. Wiley, Chichester (1997)), are found in numerical calculations. It is found that the local stress–strain state of the binder depends on the cross-sectional shape of the fibers. In particular, for fibers with a circular cross-section, one of the modes is strongly weakened. Numerical calculations do not show the presence of modes other than those described in (Kalamkarov A L, Kolpakov A G: Analysis, Design and Optimization of Composite Structures. Wiley, Chichester (1997)). If, in the case of square fibers, the assessment of the stress–strain state value is possible using simplified formulas from (Kalamkarov A L, Kolpakov A G: Analysis, Design and Optimization of Composite Structures. Wiley, Chichester (1997)), then for fibers of other sections, it is necessary to use a computer to calculate the stress–strain state.