Boundary element analysis of hyper-elastic elastomeric materials School of Engineering, Cranjkdd University, UK M.Bayliss and A. El-Zafrany Abstract cylinder is also examined to test for symmetryof the displacement solution. Rivlin strain energy formulation. The case of a pressurisedthick walled ical and numerical solutions to the standard patch test using the Mooney- method as applied to elastomers and presents a comparison between analyt- This paper develops the necessary derivations for the boundary element 1 Introduction and Ogden [ll] material models. sion ratio based strain energy formulations include the Valanis-Landel [g] or Mooney-Rivlin formulation [5]. Examples of the latter principle exten- function are the Rivlin formulation [lo] and the reduced Rivlin polynomial principalextensionratios.Examples of the former type of strain energy is taken where either the equation is based on the strain invariants or the plications a phenomenologicalapproach to the strain energy formulation are many types of material model, but generally for most numerical ap- the partial derivative of the strain energy with respect to strain [l].There methods the constitutive relationship between stress and strain is based on incompressibility. Consequently for both the finite and boundary element lems fail when Poisson’s ratio approaches 0.5 corresponding to near or total It iswell known that standard displacement formulations of elastic prob- a paper by Phan-Thien [7] which covers the application of the BEM to finite plications in finite elasticity and elastomers. Early work in the field includes although succesfully applied to many engineering problems has had few ap- The BEM (Boundaryelement method) is a relatively new technique and © 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved. Web: www.witpress.com Email [email protected] Paper from: Boundary Elements XXIV, CA Brebbia, A Tadeu and V Popov (Editors). ISBN 1-85312-914-3
Boundary element analysis of hyperelastic elastomeric materials
Jun 14, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
