The unified higher-order theory of two-phase nonlocal gradient elasticity is conceived via consistently introducing the higher-order two-phase nonlocality to the higher-order gradient theory of elasticity. The unified integro-differential constitutive law is established in an abstract variational framework equipped with ad hoc functional space of test fields. Equivalence between the higher-order integral convolutions of the constitutive law and the nonlocal gradient differential formulation is confirmed by prescribing the non-classical boundary conditions. The strain-driven and stress-driven nonlocal approaches are exploited to simulate the long-range interactions at nano-scale. A range of generalized continuum models are restored under special ad hoc assumptions. The established unified higher-order elasticity theory is invoked to analytically examine the wave dispersion phenomenon. In contrast to the first-order size-dependent elasticity model, the higher-order two-phase nonlocal gradient theory can efficiently capture the wave dispersion characteristics observed in experimental measurements. The precise description of nano-scale wave phenomena noticeably underlines the importance of applying the proposed higher-order size-dependent elasticity theory. A viable approach to tackle peculiar dynamic phenomena at nano-scale is introduced.

通过一致地将高阶两相非局部性引入到高阶弹性梯度理论中，构想出统一的两相非局部梯度弹性高阶理论。统一的积分-微分本构法是在抽象的变分框架中建立的，该框架具有试验场的临时功能空间。通过规定非经典边界条件，可以确定本构定律的高阶积分卷积与非局部梯度微分公式之间的等价关系。利用应变驱动和应力驱动的非局部方法来模拟纳米级的远程相互作用。在特殊的特殊假设下，可以恢复一系列广义的连续体模型。调用已建立的统一的高阶弹性理论来分析检查波的色散现象。与一阶依赖于大小的弹性模型相反，高阶两相非局部梯度理论可以有效地捕获在实验测量中观察到的波频散特性。纳米尺度波现象的精确描述明显地强调了应用所提出的高阶尺寸相关弹性理论的重要性。介绍了一种解决纳米尺度特殊动态现象的可行方法。纳米尺度波现象的精确描述明显地强调了应用所提出的高阶尺寸相关弹性理论的重要性。介绍了一种解决纳米尺度特殊动态现象的可行方法。纳米尺度波现象的精确描述明显地强调了应用所提出的高阶尺寸相关弹性理论的重要性。介绍了一种解决纳米尺度特殊动态现象的可行方法。