A novel phenomenological model for predicting hysteresis loss of rubber compounds obtained from ultra-large off-the-road tires

The objective of this study was to develop a novel phenomenological model that can predict the hysteresis loss of rubber compounds obtained from ultra-large off-the-road (OTR) tires under typical operating conditions at mine sites. To achieve this, first, cyclic tensile tests were conducted on tire tread compounds to derive the experimental results of hysteresis curves, peak stress, residual strain, and hysteresis loss at 6 strain levels, 8 strain rates, and 14 rubber temperatures. Then, referring to these experimental results, a phenomenological model was developed – the HLSRT model (a hysteresis loss model considering strain levels, strain rates, and rubber temperatures). This HLSRT model was generated based on a novel strain energy function that was modified from the traditional Mooney-Rivlin (MR) function, and the model was used to predict the hysteresis loss of rubber compounds in OTR tires. The prediction results show that the HLSRT model estimated the hysteresis loss of tire tread compounds with average and maximum mean absolute percent errors (MAPEs) of 11.2% and 18.6%, respectively, at strain levels ranging from 10% to 100%, strain rates from 10% to 500% s−1, and rubber temperatures from −30°C to 100°C. These MAPEs were relatively low when compared with previous studies, showing that the HLSRT model has higher prediction accuracy. For the first time, the HLSRT model derived from this study has provided a new approach to predicting the hysteresis loss of OTR tire rubbers to guide the use of OTR tires in truck haulage at mine sites.

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

MATHEMATICAL MODEL OF THE DEVELOPMENT OF A SINGLE TWIN LAYER IN METAL CRYSTALS

By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a single twin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only in relation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in the sense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.

Cellular inertia

It has been experimentally reported that chemotactic cells exhibit cellular memory, that is, a tendency to maintain the migration direction despite changes in the chemoattractant gradient. In this study, we analyzed a phenomenological model assuming the presence of cellular inertia, as well as a response time in motility, resulting in the reproduction of the cellular memory observed in the previous experiments. According to the analysis, the cellular motion is described by the superposition of multiple oscillative functions induced by the multiplication of the oscillative polarity and motility. The cellular intertia generates cellular memory by regulating phase differences between those oscillative functions. By applying the theory to the experimental data, the cellular inertia was estimated at $$m=3-6$$ m = 3 - 6 min. In addition, physiological parameters, such as response time in motility and intracellular processing speed, were also evaluated. The agreement between the experiemental data and theory suggests the possibility of the presence of the response time in motility, which has never been biologically verified and should be explored in the future.