The nonlocal strain gradient elasticity theory is used to address mechanical problems at small scales where size effects and regularization cannot be neglected. In this work, dislocations are investigated in the framework of nonlocal simplified first strain gradient elasticity. It is shown that nonlocal simplified strain gradient elasticity is the unification of the theories of Eringen’s nonlocal elasticity of Helmholtz type and simplified first strain gradient elasticity. Nonlocal simplified strain gradient elasticity contains two characteristic lengths, namely the characteristic length of nonlocal elasticity of Helmholtz type and the characteristic length of simplified first strain gradient elasticity. The advantage of nonlocal simplified first strain gradient elasticity is that the displacement, elastic distortion, plastic distortion, total stress, Cauchy stress and double stress fields of screw and edge dislocations which are calculated here are nonsingular and finite everywhere. Moreover, the Peach-Koehler force of two screw dislocations and two edge dislocations is derived and it is shown that the Peach-Koehler force is also nonsingular. Numerical examples for all dislocation fields of screw and edge dislocations in aluminum are given.

中文翻译：

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非局部简化应变梯度弹性中的位错：Eringen 遇见 Aifantis

非局部应变梯度弹性理论用于解决小尺度的力学问题，其中尺寸效应和正则化不能被忽视。在这项工作中，在非局部简化第一应变梯度弹性的框架中研究位错。结果表明，非局部简化应变梯度弹性是Eringen亥姆霍兹型非局部弹性和简化第一应变梯度弹性理论的统一。非局部简化应变梯度弹性包含两个特征长度，即亥姆霍兹型非局部弹性特征长度和简化第一应变梯度弹性特征长度。非局部简化第一应变梯度弹性的优点是这里计算的位移、弹性畸变、塑性畸变、总应力、柯西应力以及螺旋位错和刃位错的双应力场都是非奇异的且处处有限。此外，还推导了两个螺位错和两个刃位错的Peach-Koehler力，并表明Peach-Koehler力也是非奇异的。给出了铝中螺旋位错和刃位错的所有位错场的数值示例。