Fractal Descriptions of Irregular Stress-strain Relationships of Agricultural Materials

In this paper, the application of fractal geometry to irregular stress-strain relationships of agricultural materials and foods are reviewed. The irregularity and jaggedness of stress-strain curves can be quantitatively characterized by fractal dimension which has a close relation with structural features and textural properties of material. The clear advantage of fractal dimension is that it yields a single number which provides a numerical measurement of overall roughness of the curve, unlike the Fourier Transform and other shape factors that are expressed in terms of a graphical relationship or a set of numerical coefficients. By means of generized time series analysis, the direct relations between the index of power-law function of the power spectrum and fractal dimension of the stress-strain curves have been established in theory. Furthermore, some important problems, such as relation between mechanical properties and microstructure of material or food, fractal reconstruction and fractal scale limit range, are discussed. In principle, the fractal analysis and description methods could be used in characterization of other systems, such as material sound characteristics or other physical or chemical data presented in the form of a rugged relationship. These studies on unusual behavior and complexity of material are very important to revelation of physical mechanism of properties of agricultural material and food, and the research results can be used to monitor produc- tion processing.