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1

Tetragonal or hexagonal symmetry in modeling of failure criteria for transversely isotropic materials

Ganczarski A., Adamski M.

Acta Mechanica et Automatica

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2014

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Vol. 8, no. 3

125--128

EN

Present work deals with modeling of failure criteria for transversely isotropic materials. Analysis comprises two classes of symmetry: Tsai-Wu tetragonal and new Tsai-Wu based hexagonal. Detail analysis of both classes of symmetry with respect to their advantages as well as limitations is presented. Finally, simple comparison of differences between limit curves corresponding to cross sections by planes of transverse isotropy, orthotropy and shear plane is done.

2

Propagation of waves in a micropolar transversely isotropic generalized thermoelastic half-space

Kumar R., Gupta R. R.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 3

671-681

EN

Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution are also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

3

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

Merodio J., Neff P.

Archives of Mechanics

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2006

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Vol. 58, nr 3

293-303

EN

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.

4

Energy-based limit conditions for transversally isotropic solids

Kowalczyk K., Ostrowska-Maciejewska J.

Archives of Mechanics

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2002

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Vol. 54, nr 5-6

497-523

EN

Using an example of transversal isotropy, the limit condition having an energy interpretation for anisotropic bodies proposed by J. Rychlewski [11] has been illustrated. Transversal isotropy is characterized by the highest degree of symmetry, for which the spherical tensor is not any more the eigenstate of the compliance tensor C. In the case when the spectral decomposition of the compliance tensor C is taken as a main energy-orthogonal decomposition, the limit condition representing a generalization of the Maxwell-Huber-Mises condition is obtained. For a prescribed form of the limit tensor H, the Mises condition is presented in the form of a sum of elastic energies corresponding to uniquely defined energy-orthogonal parts of stress with certain weights, representing the limiting values of those energies. The effect of Burzyński's condition on the form of anisotropy and on the limit condition is discussed. Experimental tests are proposed which could be useful in determining the physical parameters describing the transversal isotropy.