Mechanism of beginning and propagation of failure in composite materials under three-axial, two-axial and uniaxial compression is considered. The beginning of failure is determined as a result of stability loss in material structure (internal instability). The analysis of internal instability is made within the framework of three-dimensional linearised theory of de-formable bodies stability. The value of failure loads and regularities of failure propagation are determined from the condition of transition of main system of equations in the system of hyperbolic type. In continual approximation composite materials are modelled by orthotropic elastic or elastic-plastic bodies with averaged constants.
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