Effective behavior of thermo-elastic tubes with wavy layers

In the present article, the homogenization of a composite star-shaped tube with numerous thin, periodic, elastic wavy layers, is presented. The composite exhibits a multiscale periodicity allowing for a multistep asymptotic homogenization scheme starting from the finest scale. The scheme gives the complete effective thermoelastic behavior of the composite. By a numerical example of a two-phase composite with sinusoidal wavy walls, whose effective behavior is an orthotropic material, the above method is illustrated.