期刊
PHYSICAL MESOMECHANICS
卷 23, 期 6, 页码 547-555出版社
SPRINGER
DOI: 10.1134/S1029959920060107
关键词
Nonlocal elasticity; Fractional calculus; Caputo derivative; Riesz derivative; Screw dislocation; Edge dislocation
Nonlocal elasticity assumes integral stress constitutive equation, takes into account interatomic long-range forces, reduces to the classical theory of elasticity in the long wave-length limit and to the atomic lattice theory in the short wave-length limit. In this paper, we propose the nonlocal elasticity theory with the kernel (the weight function in the integral stress constitutive equation) which is the Green function of the Cauchy problem for the fractional diffusion equation and is expressed in terms of the Mainardi function and Wright function being the generalizations of the exponential function. The solutions for the straight screw and edge dislocations in an infinite solid are obtained in the framework of the proposed theory.
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