Handbook of Damage Mechanics pp 395-417 | Cite as

# Micromechanics for Heterogeneous Material Property Estimation

## Abstract

There are two well-established theories in micromechanics for analytical estimation of overall property of a heterogeneous material, instead of experimental estimation; a heterogeneous material includes a partially damaged or plastically deformed material. These two theories, namely, the average field theory and the homogenization theory, are explained in this article. The average field theory is based on physical treatment of the heterogeneous material in the sense that it mimics a material sample test, and it derives a closed-form expression of the overall property in terms of the average strain and stress. The homogenization theory is based on mathematical treatment in the sense that it applies the singular perturbation expansion to the governing equations and obtains numerical solution for the overall property. In this article, the following three advanced topics are also explained: (1) strain energy consideration to obtain the consistent overall property, (2) the Hashin–Shtrikman variational principle to obtain bounds for the overall property, and (3) the extension to the overall property estimation at dynamic state from that at quasi-static state.

### Keywords

Convolution Milton Onaka### References

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