Nonlocal continuum mechanics presents still open questions about applicability of integral constitutive theories to nanostructures of current interest in Engineering Science. Nevertheless, nonlocal elasticity is widely exploited to model size effects in small-scale structures since it represents an effective tool to avoid computationally expensive procedures. The known strain-driven approach proposed by Eringen has shown an intrinsic incompatibility between constitutive and equilibrium requirements when applied to structures. Such an issue has been acknowledged by the scientific community merely for bounded continua. For structural problems defined in unbounded domains, obstruction to equilibrium caused by the strain-driven formulation is a still open issue. The present contribution definitely proves inapplicability of the strain-driven spatial convolution to structural mechanics and proposes a consistent nonlocal approach for both bounded and unbounded structures. The presented methodology is based on stress-driven spatial convolutions, representing the key paradigm to formulate a well-posed theory of integral elasticity and to effectively model scale effects in nanobeams of applicative interest in Nano-Mechanics.

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非局部梁力学的建模问题和进展

非局域连续介质力学提出了关于积分本构理论对当前工程科学感兴趣的纳米结构的适用性的悬而未决的问题。然而，非局部弹性被广泛用于模拟小规模结构的尺寸效应，因为它是避免计算昂贵的过程的有效工具。 Eringen 提出的已知应变驱动方法表明，当应用于结构时，本构要求和平衡要求之间存在内在的不兼容性。科学界仅仅因为有界连续体而承认这样的问题。对于无界域中定义的结构问题，由应变驱动公式引起的平衡阻碍仍然是一个悬而未决的问题。目前的贡献明确证明了应变驱动的空间卷积在结构力学中的不适用性，并为有界和无界结构提出了一致的非局部方法。所提出的方法基于应力驱动的空间卷积，代表了制定适定的积分弹性理论和有效模拟纳米力学应用感兴趣的纳米梁尺度效应的关键范例。