Homogenization of strength, fatigue and creep durability of composites with periodic structure

The composite macro-strength and -durability is estimated using the approximation to the micro-stress field, known from the asymptotic theory of homogenization, and presented in terms of a non-local strength and durability condition. The macro-strength and -durability functional over the homogenized stress-field is determined by micro-geometry, elastic and strength properties of the periodicity cell. The uniform in time convergence of the micro- to the macro-strength and -durability condition is also proved based on the two-scale convergence of the micro-stresses to their first approximation. Special applications to concrete and cements will be mentioned.