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The conditions for bifurcation of a circular cylindrical tube of elastic material subjected to combined axial loading and internal pressure are well known and are frequently used as a reference in related works. The present paper takes the theory further by considering a residually stressed circular cylindrical dielectric tube subjected to a combination of internal or external pressure, axial load and radial electric field. We examine axisymmetric incremental deformations and increments in the electric displacement superimposed on a known finitely deformed and residually stressed configuration in the presence of an electric field. The governing equations and boundary conditions are first obtained in general form and then specialized for the neo-Hookean and Ogden electroelastic models. The system of equations is solved numerically for different values of charge density and radial and circumferential residual stresses, and the results are compared with the purely elastic case. The bifurcation curves are presented as the azimuthal stretch on the inner surface versus the axial stretch together with the corresponding zero pressure curves. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'. [ABSTRACT FROM AUTHOR]

This paper deals with applying two main sensitivity analysis (SA) methods, namely, the Sobol method and the Fourier Amplitude Sensitivity Test (FAST) method on the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress. The mechanical side of the problem was previously proposed by Merodio & Ogden (2016). The input parameters in the form of the initial cylinder geometry, the amount of the residual stress, the azimuthal stretch, the axial elongation, and the torsional strain are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In the present work, through applying Sobol and FAST methods, the most influential factors among input parameters on the output variable have been determined. The assessment of our results is then determined by the computation of bias and standard deviation of Sobol and FAST indices for each input parameter in the model. • We study the extension, inflation, and torsion of residually stressed tubes. • The sensitivity analysis is applied to determine the sensitivity to input parameters. • The FAST method and Sobol method are applied in the sensitivity analysis. • The input parameters are distributed according to three distribution functions. [ABSTRACT FROM AUTHOR]

To test the capability of the multilayer model, we used previously published layer-specific experimental data relating to the axial pre-stretch, the opening angle, the fiber distribution obtained by polarized light microscopy measurements, and the uniaxial and biaxial response of the porcine descending and abdominal aorta. We fitted the mechanical behavior of each arterial layer using Gasser, Holzapfel and Ogden strain energy function using the dispersion parameter κ as phenomenological parameter obtained during the fitting procedure or computed from the experimental fiber distribution. A multilayer finite element model of the whole aorta with the dimensions of the circumferential and longitudinal strips were then built using layer-specific material parameters previously fitted. This model was used to capture the whole aorta response under uniaxial and biaxial stress states and to reproduce the response of the whole aorta to internal pressure. Our results show that a model based on a multilayer structure without residual stresses is unable to render the uniaxial and biaxial mechanical response of the aorta (R 2 = 0.6954 and R 2 = 0.8582 for descending thoracic aorta (DTA) and infrarenal abdominal aorta (IAA), respectively). Only an appropriate multilayer model that includes layer-specific residual stresses can reproduce the response of the whole aorta (R 2 = 0.9787 and R 2 = 0.9636 for DTA and IAA respectively). In addition, a multilayer model without residual stresses produces the same stress distribution as a monolayer model without residual stresses where the maximal value of circumferential and longitudinal stresses appears at the inner radius of the intima. Finally, if layer-specific residual stresses are not available, there is less error the stress distribution using a monolayer model with residual stresses that a multilayer model without residual stresses. [ABSTRACT FROM AUTHOR]