Geodesic
Extended Hashin-Shtrikman variational principles
Applications of Mathematics, Tome 49 (2004) no. 4, pp. 357-372.

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Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the two most important Lagrange’s and Castigliano’s variational principles are formulated in the sequel. Then the classical Hashin-Shtrikman principles are recalled and the involvement of eigenparameters is studied in more detail.
DOI : 10.1007/s10492-004-6404-z
Classification : 49S05, 74B10, 74E30, 74Q20
Keywords: extended Hashin-Shtrikman variational principle; eigenparameter; transformation field analysis 
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Procházka, Petr; Šejnoha, Jiří. Extended Hashin-Shtrikman variational principles. Applications of Mathematics, Tome 49 (2004) no. 4, pp. 357-372. doi : 10.1007/s10492-004-6404-z. http://geodesic.mathdoc.fr/articles/10.1007/s10492-004-6404-z/

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