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Fractional Mechanics of Elastic Solids: Continuum Aspects
AbstractDifferentiation and integration of noninteger orders have many applications to describe complex properties of materials, including nonlocality and long-term memory of power-law type. In this paper the author generalizes some basic notions of the theory of elasticity by using the fractional calculus to describe elastic media with power-law nonlocality. The fractional Taylor series with Caputo derivatives are used to derive the fractional equilibrium equations for stresses, and the relationship between strain tensor and displacement vector. As an example, a one-dimensional fractional model is considered and the general solutions of the fractional differential equation for displacement are suggested.
Fractional Mechanics of Elastic Solids: Continuum Aspects
AbstractDifferentiation and integration of noninteger orders have many applications to describe complex properties of materials, including nonlocality and long-term memory of power-law type. In this paper the author generalizes some basic notions of the theory of elasticity by using the fractional calculus to describe elastic media with power-law nonlocality. The fractional Taylor series with Caputo derivatives are used to derive the fractional equilibrium equations for stresses, and the relationship between strain tensor and displacement vector. As an example, a one-dimensional fractional model is considered and the general solutions of the fractional differential equation for displacement are suggested.
Fractional Mechanics of Elastic Solids: Continuum Aspects
Tarasov, Vasily E (author)
2017
Article (Journal)
English
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