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Outline
The complexity of cavities， randomness of pore distribution， and multi-scale of pore size in porous materials make it difficult to quantitatively characterize pore microstructure. In recent years， fractal theory attracts more attention because of its unique advantages in portraying the self-similarity and multi-scale of complex structures. This paper reviews the development roadmap of fractal theory and its applications on porous materials， analyzes the single and multi-fractal feature extraction and characterization methods for porous materials at different scales， summarizes some advanced engineering material applications based on multifractal optimization， and discusses the research progress in the applications of fractal theory to the characterization of mechanical， thermal and permeability properties of porous materials. During the optimization design and performance characterization process of porous materials based on fractal theory， the main issues and shortcomings including the ambiguity of correlation mechanism between micro structure and macro multi-functional characteristics， and low efficiency and accuracy for prediction models and/or optimization algorithm are pointed out. The development trend and potential engineering applications of fractal theory such as the consideration of cross-scale effect， multi-physics coupling analysis， and optimization strategy based on machine learning are prospected.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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