3 DATA FOR FINITE ELEMENT ANALYSIS

The main interest in finite element analysis from a testing point of view is that it requires the input of test data. The rise in the use of finite element techniques in recent years is the reason for the greatly increased demand for stress strain data presented in terms of relationships such as the Mooney-Rivlin equation given in Section 1 above.

Simple linear FEA programmes, as used for stress analysis of metals, take Young's modulus and Poisson's ratio as input but this is not satisfactory for rubbers because the strains involved cannot be considered as small and the Poisson's ratio is very close to 0.5. Non-linear FEA programmes for use with rubbers take data from a model such as the Mooney-Rivlin equation. More sophisticated programmes will allow a number of models to be used and may also allow direct input of the stress strain data.

For gum rubbers and lightly filled compounds, the Mooney-Rivlin equation often models the tensile stress-strain curve well up to extensions of 150% or more. However, for more highly filled compounds (and almost always for commercially important compounds) this simple function only works well up to about 50% strain. A much better fit over an extended strain range can be obtained by taking the next logical term in the infinite series of the general expression. Using:

experience at Rapra is that the stress-strain curve can usually be modeled quite accurately to strains in excess of 100%. An illustration of the...