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首页> 外文期刊>International Journal of Solids and Structures >A combined first principles and analytical determination of the modulus of cohesion, surface energy, and the additional constants in the second strain gradient elasticity
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A combined first principles and analytical determination of the modulus of cohesion, surface energy, and the additional constants in the second strain gradient elasticity

机译：结合的第一原理和内聚模量，表面能以及第二应变梯度弹性中的其他常数的解析确定

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摘要

Mindlin's (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.
机译：Mindlin（1965）的第二应变梯度理论由于具有捕获边缘，拐角和表面影响的能力而特别受关注。除了通常的Lamé常数外，在此框架中进行公式化还需要了解16种其他材料常数。迄今为止，还没有成功的实验技术来测量反映物质离散性质的这些材料参数。通过使用第一原理密度泛函理论（DFT）结合分析公式来计算原子力常数，本工作为这些参数的原子计算提供了精确的补救方法。可以看出，在第二应变梯度弹性中，由块状材料的原子晶格动力学与其对应物之间的等效性得出的一致性条件，不足以计算所有其他常数。正如将要讨论的，存在两个缺失条件，然后通过考虑表面效应的自由站立膜问题来提供。考虑到表面效应，计算出作为重要的附加常数之一的内聚模量。此外，还给出了根据内聚模量，拉梅常数，材料特征长度和膜厚度的表面能的解析表达式。如果膜厚度远大于材料的特征长度的大小，则表面能将不再取决于膜厚度。

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