A variational approach to the theory of the elastic behaviour of multiphase materials

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Abstract

Variational principles in the linear theory of elasticity, involving the elastic polarization tensor, have been applied to the derivation of upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry. When the ratios between the different phase moduli are not too large the bounds derived are close enough to provide a good estimate for the effective moduli. Comparison of theoretical and experimental results for a two-phase alloy showed good agreement.

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∗This research has been sponsored by the Office of Naval Research under Contract Nonr 551 (42) with the University of Pennsylvania, Philadelphia.

Formerly with the Franklin Institute Laboratories for Research and Development, Philadelphia.

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