Estimation of very narrow bounds to the behavior of nonlinear incompressible elastic composites |
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| Authors: | L D Pérez-Fernández J Bravo-Castillero R Rodríguez-Ramos F J Sabina |
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| Institution: | (1) Departamento de Física Aplicada, Instituto de Cibernética, Matemática y Física, 15# 551 e/ C y D, Vedado, CP 10400 Ciudad de la Habana, Cuba;(2) Departamento de Ciencias Básicas, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Estado de México, Carretera Lago de Guadalupe Km. 3.5, Atizapán de Zaragoza, Estado de México, C.P. 52926, México;(3) Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, CP 10400 Ciudad de la Habana, Cuba;(4) Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado postal 20-726, Delegación álvaro Obregón, 01000 México D. F., México |
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| Abstract: | Variational bounds for the effective behavior of nonlinear composites are improved by incorporating more-detailed morphological
information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference
material with the same microstructure as the nonlinear composite. The geometrical information is contained in the effective
properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In
this paper, the variational approach is combined with estimates for the effective properties of the reference composite via
the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear
elastic composite, significantly improving some recent results. |
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| Keywords: | Nonlinear composites Variational bounds Asymptotic homogenization Effective properties |
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