On some composite failure criteria based on the averaging method

The construction of an anisotropic criterion for composite failure is based on the use of the averaging method and micromechanical criteria for each of the components. The averaging method permits calculating not only the effective properties of a composite using the solutions of a local problem on the periodicity cell but also the stresses and strains in each composite. Using the superposition method and studying the composite brittle failure, we can calculate the stress distribution for an arbitrary radial (simple) macroloading as the linear combination of six basic problems on the periodicity cell. The limit load for an effective material is obtained from the condition that some of the composite components starts to fail. For given trajectories, the limit loads depend on the geometry of elastic properties and mainly on the ratio of ultimate strengths for different components of the composite.