To study the mechanical behavior of an incompressible polymeric degradable vessel subjected to the neo-Hookean constitutive model, two solution frameworks are introduced. One is combining a recently developed semi-analytical method and the [Formula: see text]-family time approximation (hybrid method). The other is the Standard Galerkin Finite Element Method (SGFEM), which is implemented by providing a script in the FlexPDE commercial software. A deformation-induced evolution law is used to study the dependence of material properties upon time and position in the polymeric vessel during bulk degradation. The convergence of the two proposed methods on degradable vessel responses under the axisymmetric plane-strain conditions is seen. Although the hybrid method, unlike the SGFEM, is implemented as an iteration-based algorithm, it uses highly acceptable central processing unit time because it can directly solve differential equations without converting variables. The FlexPDE method is much easier to extend to more complex case studies because the hybrid method is based on an analytical approach. It is found that less pressure is required to maintain the incompressibility of the material during the degradation. The material response to incompressibility decreases more sharply in the inner radius of the vessel. Initially, the hoop stress decreases in the inner radius but eventually reaches more than its virgin value.

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A theory is proposed to study the vibrations of homogenous isotropic circular cylindrical shells based on a developed plate vibration theory. By proposing a novel distribution of the shear stress and strain across the thickness of the shell, the arguments are adjusted such that the transverse shear strains and stresses equal zero at the shell surfaces. Due to the existing curvature in the circumferential direction, the defined shear stress and strain distributions consider a change in the position of the neutral plane toward the center of curvature. In the presented Two-Separated Lateral Displacement (TSLD) theory, the lateral displacement is defined by two bending and shear parts to provide an analytical model, referred to as the four-variable refined plate theory. The similarity to classical theory and involving only four unknowns are significant features of the introduced theory. The TSLD theory is verified against the available data in the literature. It is shown that the provided stress and stress distributions lead to more accurate results, especially in moderately thick cylinders. The proposed theory is remarkably more precise than classical shell theory and First-order Shear Deformation Theory (FSDT). Results of the TSLD theory are as accurate as the Higher-Order Shear Deformation Theory (HOST12) for the higher frequency parameters and more thick shells, while the TSLD theory implementation is much simpler than the HOST12.

The present paper investigates the degradation of compressible polymers based on the proposed model on strain-induced degradation of incompressible polymers. In a non-equilibrium thermodynamic framework, constitutive equations and evolution laws are derived using the principle of maximum energy dissipation rate and specifying how energy can be stored and dissipated. As a computational model, the governing equations are applied to the pressurized polymeric vessel subjected to the Ogden–Hill compressible hyperelastic material model. To analyze the axisymmetric plane-strain degradable vessel, programming in ANSYS Parametric Design Language (APDL) and the Standard Galerkin Finite Element Method (SGFEM) are applied. The results show that the degradable compressible Ogden–Hill model can also predict the degradation of incompressible polymers subjected to the neo-Hookean model. Results also reveal that the highest dissipation rate and material softening occur at the inner radius of the inflated degradable vessel. Creep-like and stress-relaxation-like responses of the polymeric vessel with time-position-dependent material properties are examined. ANSYS coding indicates good accuracy and efficiency in studying the compressible vessel subjected to inhomogeneous degradation.