Nonlinear multilevel combined boundary-value problems for composite mechanic are considered to predict elastic and strength properties of composites. They take into account the stage of the structure damage accumulation. Nanotechnology tendencies suggest that the development of nonlinear multilevel combined boundary-value problems is vital in view of the development of hybrid composites. To describe structural failure, calculate the deformation trajectories and predict the strength properties of composites, a new material object is used, that is a fourth rank damage function depending on the loading conditions. The supplementary conditions, which relate the structure damage tensor with invariants of the structure stress and strains tensors are written to close the equation system. For isotropic fourth-rank micro-damage tensor the brittle and viscous criterions are used. A theory of the structure damage accumulation in micro-heterogeneous solids is developed. It establishes unique relations between invariant measures of structural and macroscopic failure. Using the periodic component method, a new functional of the nonlinear combined boundary-value problem is constructed. It allows predicting effective elastic properties and constructing strength surfaces of real composites.
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