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

Abstract

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.

Evaluation of the Degree of Dispersion of Polymer Nanocomposites (PNCs) Using Nonlinear Rheological Properties by FT-Rheology

“…The analysis of distorted nonlinear stress responses is a key feature of the LAOS test. There are several ways of characterizing LAOS results, four typical responses of G ′ and G ″ as a function of strain amplitude, stress decomposition, , Chebyshev polynomials, and Fourier transform (FT)-rheology. , Among them, FT-rheology can easily quantify weak signals of higher harmonics. In particular, the normalized third-harmonic intensity by first-harmonic intensity ( I 3 /I 1 = I 3/1 ) is utilized to characterize complex fluids.…”

Clay Dispersion Assessment via FT-Rheology for Polypropylene/Clay Nanocomposites Fabricated by an Electric Field

“…Analyzing these distorted stress responses is the primary key in the LAOS test. There are several methods to characterize the LAOS test results, which are four LAOS types of responses in G ′(γ 0 ) and G ″(γ 0 ), , stress decomposition, , Chebyshev polynomials, the sequence of physical processes (SPP), , and FT-rheology. − FT-rheology has been introduced extensively because weak signals of higher harmonics can be quantified readily. The third harmonic intensity divided by the first, , i.e., I 3 / I 1 = I 3/1 , is one of the primary parameters utilized in FT-rheology.…”

A data-driven method for automated data superposition with applications in soft matter science

“…A number of previous works have made efforts to automate the process of master curve construction. These include methods based on minimizing the mean squared error between data at every state and a single basis expansion (Honerkamp and Weese, 1993; Buttlar et al, 1998; Sihn and Tsai, 1999), methods for minimizing the area between linear interpolants defined by data at different states (Barbero and Ford, 2004; Gergesova et al, 2011; Gergesova et al, 2016), methods for minimizing the mean squared error between the derivatives of spline interpolants fit to the data (Hermida and Povolo, 1994; Naya et al, 2013), methods to minimize the arc length between data sets at different states (Cho, 2009; Maiti, 2016), and a method that leverages mathematical constraints on the Fourier transform of real-valued time-series data (Rouleau et al, 2013). However, only a few of these methods have been demonstrated for simultaneous horizontal and vertical shifting, and many require either parameters, an appropriate interpolant, or a set of basis functions to be specified by the user, thereby introducing elements of subjectivity into the methodology.…”