Notes on the lateral contraction of linear isotropic visco-elastic materials

Visco-elastic materials can be investigated using creep experiments or stress relaxation experiments. In both experimental types of the phenomenon called lateral contraction occurs. Because the two types are known to be different, we need to distinguish two material functions to describe lateral contraction, namely a creep contraction ratio and a stress relaxation contraction ratio. Expressions are derived that describe how for linear and isotropic visco-elastic materials these functions depend on other material functions. It is demonstrated that these two possible contraction ratios are different functions. The contraction ratio based on the stress relaxation experiment is found to be the visco-elastic analogue of the clastic constant called Poisson''s ratio.