Abstract
The present paper deals with the dynamic inflation of rubber-like membranes.The material is assumed to obey the hyperelastic Mooney's model or the non-linear viscoelastic Christensen's model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite-difference algorithm for the time-integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas flow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through different examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber-like membranes. Copyright © 2001 John Wiley & Sons, Ltd.
Highlights
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Wineman [5] and Feng [6] used semi-analytical time-discretization schemes to solve the time-dependent in ation of an initially plane circular non-linear viscoelastic membrane
Rubber-like materials are assumed to obey non-linear integral viscoelastic constitutive equations such as K-BKZ and Christensen’s models
Summary
The general constitutive equation of an isotropic, homogeneous, incompressible simple material is a tensor function of the strain history [10]: S(t) = −pC−1(t) + S {C( )}. 6t in which C(t) is the right Cauchy–Green deformation tensor at time t; p is an indeterminate hydrostatic pressure due to the incompressibility assumption, S(t) stands for the second Piola–Kirchho stress tensor and S is the response functional. Noting F(t) the deformation gradient and J (t) the Jacobian of the transformation (determinant of F(t)), the stress tensor S(t) is related to the true stress tensor (t) by. In the two sections, we present two classical types of behaviour used to describe rubberlike materials such as natural rubber, elastomeric materials or high-temperature thermoplastics: hyperelastic and non-linear viscoelastic constitutive relations
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