Recent studies on localized bulging in inflated membrane tubes have shown that the initiation pressure for the onset of localization is determined through a bifurcation condition. This kind of localization has also been shown to be much more sensitive to geometrical and material imperfections than classical sub-critical bifurcation into periodic patterns. We use these results to show that the initial formation of aneurysms in human arteries may also be modeled as a bifurcation phenomenon. This bifurcation interpretation could provide a theoretical framework under which different mechanisms leading to, or reducing the risk of, aneurysm formation can be assessed in a systematic manner. In particular, this could potentially help in assessing the integrity of aneurysm repairs.

A kink is a singular surface across which the displacement is continuous but the deformation gradient and the fibre direction suffer a discontinuity. A kink band is a highly deformed or even damaged region bounded by two kinks. The objective of modelling kink-band formation, within the framework of finite elasticity theory, is to find a suitable strainenergy function, guided by results from a finite number of simple experiments, that can be used to predict what have been observed and what might be possible under other loading conditions. In this paper, we explain a theoretical basis for choosing such strain-energy functions. More precisely, for a given strain-energy function that allows formation of kinks and a given deformation field, we characterize all possible deformation fields that can join the given deformation field through a kink and explain a procedure that can be used to assess the stability properties of any kink solution that is mathematically possible. In contrast with most previous studies in the engineering community where, for instance, the kink orientation angle is undetermined, the present theory completely determines the kink propagation stress, the kink orientation angle and the fibre direction within the kink band.

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This work continues our study of woven fabric buckling and provides generally analytical results on the buckling of a woven fabric sheet subjected to simple shear along the direction making an angle, θ(0° ≤ θ < 90°) say, to the warp. The buckling direction is related to the angle 0 and the critical amount of shear. As an illustration, the curve of the buckling direction angle versus the amount of shear for θ = 30° is plotted. Out-of- plane fabric buckling is possible, and only a flexural buckling mode can occur. The buckling condition for the flexural mode is also obtained and, as an illustration, a curve for 0 = 30° is plotted. This work also provides foundations for numerical methods to simulate KES shear buckling for fabric.

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