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Evaluations and Bounds on Elastic Moduli of Heterogeneous Materials

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Micromechanics of Composite Materials

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 186))

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Abstract

This chapter is concerned with composites and polycrystals, consisting of two or more distinct phases that have known stiffnesses L r defined in the fixed overall coordinate system of a representative volume V. Phase volume fractions C r \( \Sigma_{{r = 1}}^n\,{c_r} = 1, \) are no longer small, hence evaluation of both overall properties and local fields must reflect interactions between individual phase volumes. Spatial distribution of the phases in V is statistically homogeneous, as described in Sect. 3.2.2, and perfect bonding is assumed at all interfaces. Of interest are derivations of upper and lower bounds on the overall stiffness \( {L} = {{L}^{\text{T}}} \) and compliance \( {M} = {{L}^{{ - 1}}} \) of the aggregate, and of estimates of phase volume averages of strain and stress fields, caused in the heterogeneous system by application of uniform overall strain \( {{\varepsilon }^0} \) or stress \( {{\sigma }^0} \). Those are sought in terms of known volume fractions, elastic moduli, shape and alignment of the constituent phases, Sects. 6.1 and 6.2.

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  1. Mechanical, Aeronautical and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    George J. Dvorak

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  1. George J. Dvorak
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Dvorak, G.J. (2013). Evaluations and Bounds on Elastic Moduli of Heterogeneous Materials. In: Micromechanics of Composite Materials. Solid Mechanics and Its Applications, vol 186. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4101-0_6

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  • DOI: https://doi.org/10.1007/978-94-007-4101-0_6

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