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Applied Scientific Research

, Volume 48, Issue 2, pp 193–210 | Cite as

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

  • Peter A. A. van Hoogstraten
  • Paul M. A. Slaats
  • Frank P. T. Baaijens
Article

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 an algorithm to calculate stresses in the rubber material from velocities instead of displacements. This problem is solved with an 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 implementations are compared with results obtained by a standard Lagrangian approach finite element package and good agreement has been found.

Keywords

Convection Rubber Element Modelling Finite Element Modelling Test Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

C

material parameter

I1,I2

first, second invariant ofB

w,q

weighting function

t

time

W

strain energy function

n

unit outward normal

t

surface traction vector

u

velocity vector field

w

weighting vector

x

position vector field

α

interpolation parameter

ε

penalty parameter

Δt

timestep

B

left Cauchy-Green tensor

D

rate of strain tensor

I

unity tensor

F

deformation gradient

σ

Cauchy stress tensor

τ

stress tensor

Ω

rate of rotation tensor

()T

transpose

(′)

time derivative

gradient operator

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Peter A. A. van Hoogstraten
    • 1
  • Paul M. A. Slaats
    • 1
  • Frank P. T. Baaijens
    • 1
    • 2
  1. 1.Faculty of Mechanical Engineering, Section of Engineering FundamentalsEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Philips Research LaboratoriesEindhovenThe Netherlands

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