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Ponte Castañeda, P.

New variational principles in plasticity and their application to composite materials. (English) Zbl 0764.73103

J. Mech. Phys. Solids 40, No. 8, 1757-1788 (1992).
A variational method for bounding the effective properties of nonlinear composites with isotropic phases, proposed recently by the author [J. Mech. Phys. Solids 39, No. 1, 45-71 (1991; Zbl 0734.73052)], is given full variational principle status. Two dual versions of the new variational principles are presented and their equivalence to each other, and to the classical variational principles, is demonstrated. The variational principles are used to determine bounds and estimates for the effective energy functions of nonlinear composites with prescribed volume fractions in the context of the deformation theory of plasticity.

Cited in 3 Reviews
Cited in 64 Documents

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74R20 Anelastic fracture and damage
74E30 Composite and mixture properties

Keywords:

nonlinear Hashin-Shtrikman bounds; isotropic, particle-reinforced composites; transversely isotropic, fiber-reinforced composites; nonlinear composites; isotropic phases; bounds; estimates; effective energy functions; prescribed volume fractions; deformation theory

Citations:

Zbl 0734.73052
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Full Text: DOI

References:

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