Large Deformation Analysis for a Cylindrical Hyperelastic Membrane of Rubber-Like Material under Internal Pressure

2001 ◽  
Vol 74 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Xiaoping Guo
Keyword(s):  
Numerical Solution ◽  
Large Deformation ◽  
Initial Guess ◽  
Axisymmetric Deformation ◽  
Deformation Field ◽  
Deformation Analysis ◽  
Lagrangian Formalism ◽  
Equilibrium Path ◽  
Governing Equations ◽  
Deformation Instability

Abstract This work studies the large deformation of a cylindrical hyperelastic membrane circumferentially bonded and sealed at each end to a rigid tube. The membrane is subjected to the delivery of an inflating fluid through the tubular channel, causing it to undergo the large, quasi-static axisymmetric deformation. The membrane is made from a rubberlike material and assumed to be isotropic and incompressible. The Lagrangian formalism is employed to develop geometric relations of the deformation field and the system of governing equations in terms of principal stretches and Cauchy stresses. With the material's constitutive laws and proper boundary conditions, the incorporation of the geometric relations and governing equations is made to derive the numerical solution system of the deformation field in the form of two-point boundary-value problem as composed of four first-order ordinary differential equations. Special attention is given to relevant numerical formulation. The Newton-Raphson iterative algorithm, together with the fourth-order Runge—Kutta algorithm, is utilized. A geometric approximation on an inflated bulge is presented to give an initial guess to a deformed membrane profile. In an attempt to obtain convergent behavior of numerical solution along the equilibrium path of deformation, a displacement control strategy is suggested to mimic the quasi-static volume-controlled inflation process. Numerical results are presented. The occurrence of deformation instability is discussed. The effects of various strain energy density functions on inflation kinematics are analyzed.

scholarly journals Bias Truck Tire Deformation Analysis with Finite Element Modeling

2020 ◽  
Vol 10 (12) ◽  
pp. 4326
Author(s):  
Józef Pelc
Keyword(s):  
Incompressible Material ◽  
Axisymmetric Deformation ◽  
Thermal Shrinkage ◽  
Deformation Analysis ◽  
Truck Tire ◽  
Non Linear ◽  
Strain Relationship ◽  
Tire Modeling ◽  
Total Lagrangian Formulation

This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.

Large deformation analysis of moderately thick viscoelastic plates

2019 ◽  
Vol 163 ◽  
pp. 146-167 ◽  
Author(s):  
Nasrin Jafari ◽  
Mojtaba Azhari ◽  
Bijan Boroomand
Keyword(s):  
Large Deformation ◽  
Deformation Analysis ◽  
Large Deformation Analysis

scholarly journals Mechanical Property Analysis of Circular Polymer Membrane under Uniform Pressure

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Sang Jianbing ◽  
Li Xiang ◽  
Xing Sufang ◽  
Wang Wenjia
Keyword(s):  
Mechanical Property ◽  
Polymer Material ◽  
Vertical Displacement ◽  
Polymer Membrane ◽  
Constitutive Parameter ◽  
Deformation Analysis ◽  
Strengthening Effect ◽  
Uniform Pressure ◽  
Governing Equations ◽  
Property Analysis

Mechanical property analysis of circular hyperelastic polymer membrane under uniform pressure has been researched in this work. The polymer membrane material is assumed to be homogeneous and isotropic and incompressibility of materials has been considered. Based on the modified stain energy function from Gao and nonmomental theory of axial symmetry thin shell, finite deformation analysis of polymer membrane under uniform pressure has been proposed in current configuration and governing equations of polymer membrane have been achieved. By utilizing the boundary condition, theoretical results of governing equations have been obtained and vertical displacement distribution and stress distribution have been achieved. The results show that the constitutive parameternhas a strengthening effect on the polymer material and the constitutive parameterαplays a controlling role for the second strain invariantI2, which also has a strengthening effect on the polymer material. This research has revealed the deformational mechanism of polymer membrane and provided reference for the design of polymer membrane.

Meshless TL and UL Approaches for Large Deformation Analysis

2010 ◽  
Vol 139-141 ◽  
pp. 893-896 ◽  
Author(s):  
Yuan Tong Gu
Keyword(s):  
Large Deformation ◽  
Computational Efficiency ◽  
Metal Forming ◽  
Weak Form ◽  
Superior Performance ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Updated Lagrangian ◽  
Local Weak Form ◽  
Large Deformation Problems

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using in the UL approach than using in the TL approach.

Sign in / Sign up

Export Citation Format

Share Document