Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Archives of Mechanics

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: loss of ellipticity

Sortuj według:

Ogranicz wyniki do:

A note on tensile instabilities and loss of ellipticity for a fiber-reinforced nonlinearly elastic solid

Merodio J., Neff P.

Archives of Mechanics

2006

Vol. 58, nr 3

293-303

In this paper we examine the loss of ellipticity and the associated failure of fiber-reinforced compressible nonlinearly elastic solids under deformations leading to fiber extension. In particular, the analysis concerns a material model that consists of an isotropic base material augmented by a reinforcement depending on the fiber direction and referred to as a reinforcing model. We examine a reinforcement that introduces additional stiffness under simple shear deformations in the fiber direction. In previous contributions it was shown for this material that loss of ellipticity under uniaxial tensile loading in the fiber direction requires a non-convex reinforcing model. Here we generalize this result and show that loss of ellipticity under plane deformations not associated with uniaxial loading in the fiber direction but also creating fiber extension may occur for convex reinforcing models.

Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation

Merodio J., Ogden R. W.

Archives of Mechanics

2002

Vol. 54, nr 5-6

525-552

Material instabilities in fiber-reinforced nonlinearly elastic solids are examined under plane deformation. In particular, the materials under consideration are isotropic nonlinearly elastic models augmented by a function that accounts for the existence of a unidirectional reinforcing. This function describes the anisotropic (transversely isotropic) character of the material and is referred to as a reinforcing model. The onset of failure is signalled by the loss of ellipticity of the governing differential equations. Previous work has dealt with the analysis of specific reinforcing models and has established that the loss of ellipticity for such augmented isotropic materials requires contraction in the reinforcing direction. The loss of ellipticity was related to fiber kinking. Here we generalize these results and establish sufficient conditions for the ellipticity of the governing equations of equilibrium for more general reinforcing models to be guaranteed. We also establish necessary conditions for failure of ellipticity. The incipient loss of ellipticity is interpreted in terms of fiber kinking, fiber de-bonding, fiber splitting and matrix failure in fiber-reinforced composite materials. Attention is restricted to incompressible materials in this paper.