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3D hybrid semi-analytical creep, dissipation, and dynamic stress analyses of abruptly pressurized finite-length thick visco-hyperelastic cylinders

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Abstract

The 3D creep and dynamic displacements and stresses of the suddenly pressurized “finite-length” thick visco-hyperelastic cylinders with fixed ends are investigated here for the first time, employing a hybrid semi-analytical approach. By incorporating the incompressibility condition of the material and the hierarchical Prony-series-type Mooney–Rivlin constitutive model, the dynamic 3D visco-hyperelasticity equations of the vessel are interpreted in terms of the instantaneous axial and radial time variations of the radii. The heredity integral is written in terms of the time-derivative of the relaxation kernel rather than the time derivatives of the stresses, for the first time. The resulting nonlinear integrodifferential governing equations whose number of terms grows with time are solved by an iterative solution that uses a point-collocation technique, the time-domain trapezoidal technique, and the Runge–Kutta time-marching method. Comprehensive parametric studies are performed to evaluate the effects of various geometric, hyperelastic, and viscous/creep material properties on the creep and dynamic/vibration responses of the structure. Results show that (1) in comparison with the traditional structures, the effects of the superimposed higher vibration modes and damping are much more notable in visco-hyperelastic structures, (2) the displacement and stress components are affected by not only radial inflation but also the time-dependent magnitude and sign of the bending-inspired curvatures, (3) the largest hoop and axial stresses occur in regions located about the mid-length section and in the vicinity of the fixed ends, respectively, and (4) the displacements and stresses increase but the thickness reduction decreases by increasing the cylinder length. The creep results show while the slopes of the creep curves are larger for longer cylinders, the shorter cylinder reaches the steady state earlier.

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  1. Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, 19991-43344, Iran

    M. Shariyat & M. Yazdani Ariatapeh

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  1. M. Shariyat
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Shariyat, M., Yazdani Ariatapeh, M. 3D hybrid semi-analytical creep, dissipation, and dynamic stress analyses of abruptly pressurized finite-length thick visco-hyperelastic cylinders. Acta Mech 234, 6451–6480 (2023). https://doi.org/10.1007/s00707-023-03717-w

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