Abstract Interfacial tractions generated at the interface in two-layered nanobeams are studied through the stress-driven nonlocal theory of elasticity and an interface model. The model uses a layerwise description of the problem and satisfies the continuity conditions at the interface. The size-dependency are incorporated into formulation through a nonlocal constitutive law which defines the strain at each point as an integral convolution in terms of the stresses in all the points and a kernel. The Bernoulli-Euler beam theory is used separately for each layer to describe kinematic field, and to derive size-dependent system of coupled governing equations. The displacement components within the layers are derived and the interfacial tractions are obtained through the interfacial constitutive relations. Results are presented for the interfacial shear and normal tractions, exhibiting a different behavior at the nano-scale compared to those of the layered beams with large-scale dimensions including different maximum interfacial tractions and the location where maxima occur. A superior resistance of nanobeams against debondings and delaminations due to the interfacial normal tractions compared to that of the beams with large-scale dimensions is observed. The formulation and the understandings presented here are expected to stimulate further researches on multilayered nanobeams, including their interfacial fracture mechanics.

中文翻译：

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分层纳米梁中界面牵引的非局部分层公式

摘要 通过应力驱动的非局域弹性理论和界面模型研究了在两层纳米梁界面处产生的界面牵引。该模型使用问题的分层描述，并满足界面处的连续性条件。通过非局部本构定律将尺寸相关性纳入公式，该定律将每个点的应变定义为所有点和内核中应力的积分卷积。Bernoulli-Euler 梁理论单独用于每一层来描述运动场，并推导出与尺寸相关的耦合控制方程系统。通过界面本构关系推导出层内的位移分量并获得界面牵引力。结果显示为界面剪切力和法向牵引力，与具有大尺度尺寸的分层梁相比，在纳米尺度上表现出不同的行为，包括不同的最大界面牵引力和出现最大值的位置。观察到与具有大尺寸尺寸的梁相比，纳米梁对由于界面法向牵引引起的脱粘和分层具有优异的抵抗力。预计这里提出的公式和理解将刺激对多层纳米梁的进一步研究，包括它们的界面断裂力学。观察到与具有大尺寸尺寸的梁相比，纳米梁对由于界面法向牵引引起的脱粘和分层具有优异的抵抗力。预计这里提出的公式和理解将刺激对多层纳米梁的进一步研究，包括它们的界面断裂力学。观察到与具有大尺寸尺寸的梁相比，纳米梁对由于界面法向牵引引起的脱粘和分层具有优异的抵抗力。预计这里提出的公式和理解将刺激对多层纳米梁的进一步研究，包括它们的界面断裂力学。