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Fractals for the Sustainable Design of Engineered Particulate Systems

The engineering properties of particulate materials are the collective manifestation of interactions among their constituent particles and are structures within which particles adopt their spatial arrangement. For the first time in the literature, this paper employs an extended concept of ‘fractals’ to show that materials constituting particles of a certain size can be rationalized in three universal fractals. Within each fractal, materials build repeatable, reproducible, and predictable traits, and exhibit the stress-strain behaviors of nondifferentiable, self-similar trajectories. We present experimental evidence for such repeatable traits by subjecting six different particulate materials to static undrained isotropic, static undrained anisotropic, and cyclic undrained isotropic stresses. This paper shows that universal fractals are associated with fractal structures; herein, we explore the matters that influence their spatial arrangement. Within the context of sustainable design, ways of engineering natural particulate systems to improve a product’s physical and hydromechanical properties are already well established. In this review, a novel extended concept of fractals is introduced to inform the biomimetic design of particulate systems, to show how biomimicry can benefit in preserving general behavioral traits, and how biomimicry can offer predicated forms, thereby enhancing the design efficiency. To pursue such an ideal, processes that lead to the engineering of natural materials should not compromise their loyalty to the parent universal fractal.