Kyrylych Tamara, Povstenko Yuriy
Department of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland.
Materials (Basel). 2025 Apr 9;18(8):1717. doi: 10.3390/ma18081717.
The constitutive equation for a nonlocal stress tensor is represented as an integral with the suitable kernel function. In this paper, the nonlocality kernel is chosen as the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter. The solutions of nonlocal elasticity problems for the straight wedge and twist disclinations in an infinite medium are obtained in the framework of this new nonlocal theory of elasticity. The Laplace integral transform with respect to the nonlocality parameter is used. It is necessary to emphasize that the transition from the nonlocal to local stress tensor is described by the limiting value of the nonlocality parameter τ→0. The obtained stress fields do not contain nonphysical singularities at the disclination lines.
非局部应力张量的本构方程表示为具有合适核函数的积分形式。在本文中，非局部核被选为关于非局部参数具有卡普托导数的分数阶扩散方程柯西问题的格林函数。在这种新的非局部弹性理论框架下，得到了无限介质中直楔形位错和扭转位错的非局部弹性问题的解。使用了关于非局部参数的拉普拉斯积分变换。需要强调的是，从非局部应力张量到局部应力张量的转变由非局部参数τ→0时的极限值描述。所得到的应力场在位错线处不包含非物理奇点。
