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.
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