Abstract
The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.
Highlights
Mandelbrot proposed the concept of fractal in 1975, which refers to the graph, phenomenon, or process with self-similarity [1]
The fractal analysis methods applied to inorganic materials such as metals and ceramics, polymers, and their composites are reviewed by the aspects of the basic theory of fractal and fractal feature extraction
The above research shows that the property change or failure of metal packaging material can be characterized by its fractal dimension, which could be obtained by box counting dimension, correlation dimension, and Hurst index; material damage has the characteristics of transition from single fractal to MF, which can be quantified by fractal dimension, and MF analysis is a relatively new research direction on the property’s analysis of metal packaging materials
Summary
Mandelbrot proposed the concept of fractal in 1975, which refers to the graph, phenomenon, or process with self-similarity [1]. The surface morphologies of all kinds of packaging materials are complex and irregular, but they have features of self-similarity, which is highly appropriate for analysis by fractal theory. Scale invariant is the property that the shape, irregularity, and complexity of an object will not change if it is enlarged or shrunk in any local area of the object. This object can have fractal features in a scale invariant range. In the measurement theory, when the measures studied are the same in unlike scales, or at least the same in statistics, it can be said that the measures studied are self-similar, which is called multifractal (MF). MF can be expressed by generalized dimension spectrum(q-Dq) or α-f(α) multifractal spectrum [17]
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