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A Eulerian approach to the finite element modelling of neo-Hookean rubber material

Technische Universiteit Eindhoven, Instituut Vervolgopleidingen
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  • Mechanical Engineering: Report Series
  • Materials Science: Report Series
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Onderzoekersopleiding Fundamentele Werktuigkunde A EULERIAN APPROACH TO THE FINITE ELEMENT MODELLING OF NEO-HOOKEAN RUBBER MATERIAL Peter A.A. van Hoogstraten CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG Hoogstraten, Peter A.A. van A Eulerian approach to the finite element modelling of neo-Hookean rubber material / Peter A.A. van Hoogstraten. - Eindhoven : Instituut Vervolgopleidingen, TUE. -111. Met lit.opg. SISO 650.2 UDC 621.3:678.4 Trefw.: eindige elementen methode / rubber. ISBN 90-5282-055-4 Abstract A Eulerian approach is applied to the finite element modelling of neo-Hookean rubber material. Two major problems are encountered. The first problem is the construction of a n algorithm to calculate stresses in the rubber material from velocities instead of displacements. This problem is solved with a n algorithm based on the definition of the velocity gradient. The second problem is the convection of stresses through the finite element mesh. This problem is solved by adapting the so-called Taylor-Galerkin technique. Solutions for both problems are implemented in a finite element program and their validity is shown by test problems. Results of these iinplementations are compared with results obtained by a standard Lagrangian approach finite element package and good agreement has been found. -iv- -V- Table of Contents O. 1 . 2. 3. 4. 5. 6. 7. General Introduction Introduction: Statement of the problem Balance laws and the neo-Hookean constitutive equation The Eulerian approach: Derivation of the velocity-stress algorithm 3.1 Incrcinental objectivity of the algorithm 3.1.1 Rigid body rotation 3.1.2 Uniform isovolumetric elongation The Eulerian approach: Convection of stresses Implementation aspects Test problem Conclusions References Page 1 5 9 1 1 14 14 16 19 23 25 31 33 Appendix A: Incremental objectivity of the stress algorithm Appendix B: PC-MATLAB Tiles B.l: Rigid body

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