Geometric insights on viscoelasticity: Symmetry, scaling and superposition of viscoelastic functions

The physical properties of viscoelastic material are functions of various variables, such as strain, strain rate, stress, temperature, pressure and so on. In this reason, it is difficult to interpret rheological behavior of viscoelastic materials. In order to realize the relation between viscoelasticity and their variables more clearly, it is often employed to reduce or simplify the effects of variables. Sometimes, geometrical insight for rheological behavior provides more clear and easy ways of interpretation. Cho et al.(2005) have suggested stress decomposition from the concept of the symmetry of shear stress. It means that shear stress changes its direction according to that of strain, and it is commonly cross lips as having odd symmetry. From the concept of dimensionless variables, the scaling rules for large amplitude oscillatory shear flow have been suggested (Cho et al. 2010). The scaling relations show that the dimensionless variables make the superposition possible regardless of frequency and strain amplitude. Additionally, geometrical insight of arc length of path which is formed by connecting data points plays a role as a criterion for TTS (time-temperature superposition) (Cho 2009). The suggested algorithm was carried out in two ways, and the validity of them is checked.