Numerical calculation of the effective coefficient in the problem of linear elasticity of a composite material

We consider the numerical calculation of the effective coefficient of the linear elasticity problem on a representative volume element having a similar volume fraction of fibers. The obtained effective coefficient is used to solve the complete problem on a coarse grid. As an example, the problem of calculating the deformation of a concrete block with the inclusion of steel fibers under the action of a three-point bending is considered. The computational implementation of the problem is carried out by the finite element method using the FEniCS computing platform.