On the Influence of Initial Stresses on the Velocity of Elastic Waves in Composites

The paper is devoted to the problem of propagation elastic waves in composites with initial stresses. We suppose stresses are well within regime. deal long-wave case and use asymptotic homogenization technique based on two-scale approach. main lies solving local (cell) problem, i.e., boundary value a periodically repeating fragment composite. In general, cannot be solved explicitly. our work, it obtained for any formulas, which convenient by standard codes. An analytical solution small Asymptotic expansions used parameter characterizing smallness zero approximation, without considered; first approximation takes into account their influence propagation. Two particular cases considered detail: laminated media frame (honeycomb cell) composites. analyzed composite can modeling porous media. select these two following reasons. First, material widely practice. Second, materials, homogenized coefficients may computed explicit form an arbitrary dependence velocity homogeneous bodies differs. tension increases both cases, but quantitative effect increase vary greatly. For bodies, or decrease (the decreases body inverted honeycomb periodicity cell). impossible under consideration related, particular, core sample analysis geophysics. This question discussed paper. also some features applications procedure dynamical stressed nonadditivity sum operators.