The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments

The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter ϵ > 0 , which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as ϵ → 0 . As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.