农业物料不规则应力应变关系的分形描述问题

Fractal Descriptions of Irregular Stress-strain Relationships of Agricultural Materials

提出了分形几何在农业物料和食品的不规则应力应变关系研究中的应用,指出分维既可以作为应力应变曲线的不规则程度的定量描述的有效手段,而且与物料或食品的结构特征和质构特征密切相关。文中对物料力学特性与微结构的相关性、分形重构以及分形上下尺度界限等有待深入研究的重要方面进行了讨论。

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.