- Asymptotic Homogenisation in Strength and Fatigue Durability Analysis of Composites (2003)
- Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength and fatigue damage measure as the structure period tends to zero is proved and their limiting values are estimated.
- Homogenization for contact problems with periodically rough surfaces (2004)
- We consider the contact of two elastic bodies with rough surfaces at the interface. The size of the micropeaks and valleys is very small compared with the macrosize of the bodies’ domains. This makes the direct application of the FEM for the calculation of the contact problem prohibitively costly. A method is developed that allows deriving a macrocontact condition on the interface. The method involves the twoscale asymptotic homogenization procedure that takes into account the microgeometry of the interface layer and the stiffnesses of materials of both domains. The macrocontact condition can then be used in a FEM model for the contact problem on the macrolevel. The averaged contact stiffness obtained allows the replacement of the interface layer in the macromodel by the macrocontact condition.
- Homogenization in elasto-plasticity (2008)
- The theory of the two-scale convergence was applied to homogenization of elasto-plastic composites with a periodic structure and exponential hardening law. The theory is based on the fact that the elastic as well as the plastic part of the stress field two-scale converges to a limit, which is factorized by parts, depending only on macroscopic characteristics, represented in terms of corresponding part of the homogenised stress tensor and only on stress concentration tensor, related to the micro-geometry and elastic or plastic micro-properties of composite components. The theory was applied to metallic matrix material with Ludwik and Hocket-Sherby hardening law and pure elastic inclusions in two numerical examples. Results were compared with results of mechanical averaging based on the self-consistent methods.