Elasticity of Fractal Material by Continuum Model with Non-Integer Dimensional Space

Abstract

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

28 pages, LaTeX. arXiv admin note: substantial text overlap with arXiv:1503.02022, arXiv:1503.02842

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Cited by in corpus (2)

• Vanishing in Fractal Space: Thermal Melting and Hydrodynamic Collapse
• Fractatomic Physics: An Invitation with Atomic Stability and Rydberg States in Fractal Spaces