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

Keywords:
numerical homogenization, linear elasticity, composite material, mathematical modeling, effective coefficient

### Abstract

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.

### References

Received

10-04-2017

How to Cite

*Mathematical notes of NEFU*, 24(2), pp. 75-84. doi: https://doi.org/10.25587/SVFU.2017.2.9247.

Issue

Section

Mathematical Modeling

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