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A laboratory programme of uniaxial, triaxial, cyclic and Brazilian tests was conducted to investigate the anisotropic mechanical behaviour of the Tournemire argillite, with different axial loading orientations with respect to the bedding planes (i.e. loading orientation angle, u ¼ 08, 308, 458, 608 and 908). The experimental results show that both strength and deformation of the argillite are direction-dependent. Failure occurs in a brittle manner with a sudden collapse of the material strength. The failure mode exhibits localization along distinct failure planes and also depends on the loading orientation. This paper summarizes the experimental results and describes constitutive relationships that were developed in order to simulate the stress -strain behaviour of the Tournemire argillite. A microstructure tensor approach is adopted in order to take into account the anisotropic behaviour of the argillite. The identification procedure for material function and parameters is outlined, and the model is applied to simulate the set of triaxial tests performed at different levels of confining pressure and orientation of the bedding planes. It is demonstrated that the model adequately reproduces the anisotropy, the pre-peak stress -strain response and the onset of material collapse in those tests.Gold Open Access: This article is published under the terms of the CC-BY 3.0 license.

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In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the rz-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field.