Effective characteristics and stress concentrations in materials with self-similar microstructure

摘要: Abstract It is proposed to model materials with self-similar structure by a continuum sequence of continua increasing scales each determined its own size the averaging volume element. The scaling represented power laws exponents microstructure, but not necessarily material fractal dimension. for tensors are shown be always isotropic (the same exponent all non-zero components) prefactors accounting anisotropy. For distributions pores, cracks and rigid inclusions elastic characteristics were using differential self-consistent method. Stresses defined in (and measured conventional units stress) law controlling transition from one another, i.e. stress field another. In case strong self-similarity uniform, coincides average (nominal) controlled sectional dimension material. Within concentrators––point force, dislocation, semi-infinite crack––produce singularities. However, as point singularity approached, finer necessary, resulting, some cases, apparent non-conventional increase.