APPLICATIONS OF FRACTIONAL CALCULUS TO THE THEORY OF VISCOELASTICITY
APPLICATIONS OF FRACTIONAL CALCULUS TO THE THEORY OF VISCOELASTICITY
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DOI：
10.1115/1.3167616
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发表时间：
1984-01-01
影响因子：
2.6
通讯作者：
KOELLER, RC
中科院分区：
文献类型：
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作者：
KOELLER, RC
分数阶微积分和阿贝尔积分方程的理论之间的连接显示的材料与记忆。得到了蠕变函数和松弛函数的表达式，其形式为依赖于分数阶导数参数β的Mittag-Leffler函数。当记忆参数β在0.05-0.35的范围内时，这些蠕变和松弛函数允许在许多十倍间隔内发生显著的蠕变或松弛。结果表明，分数阶微积分本构方程允许从固态到流体状态的连续过渡时，记忆参数从零到一。
The connection between the fractional calculus and the theory of Abel’s integral equation is shown for materials with memory. Expressions for creep and relaxation functions, in terms of the Mittag-Leffler function that depends on the fractional derivative parameter β, are obtained. These creep and relaxation functions allow for significant creep or relaxation to occur over many decade intervals when the memory parameter, β, is in the range of 0.05–0.35. It is shown that the fractional calculus constitutive equation allows for a continuous transition from the solid state to the fluid state when the memory parameter varies from zero to one.