New Variational Principles in Heterogeneous Elasticity Derived by Lagrange’s Multiplier Method

Summary

In a series of papers Hashin and Shtrikman have proposed powerful variational principles for the heterogeneous linear elasticity. These variational principles originate from Brown’s dielectric principle and are of great interest for the derivation of the elastic effective moduli of statistically homogeneous materials.

The goal of the present paper is to show how the variational principles of Hashin and Shtrikman can be derived via Lagrange multipliers. This is of importance for the further extention of this type of variation principles.