Abstract Understanding the effects of defects is crucial due to their deliberate or unintentional presence in many materials. Classical theory of elasticity may not be the best candidate to describe behaviour of structures with defects of comparable size of its underlying material organization, as it lacks in internal scale parameters. In this respect, present study focused on comparison of two well-established non-local theories; ’implicit/weak’, as micropolar (Cosserat), and ’explicit/strong’, as Eringen’s, models with that of classical model to highlight their differences in a common case study: infinite plates weakened with an elliptic hole of different aspect ratios, under remote uniaxial tension. Fraction coefficient, providing identical stress concentration factor with micropolar plates, is searched for two-phase local/nonlocal Eringen’s model. Results are obtained by adopting finite element method with quadrilateral elements. To account for the discontinuities within domain, Eringen’s model is modified by using geodetical distance instead of Euclidean one, and computationally very efficient procedure is developed to exploit the symmetric character of the problem without losing long-range interactions. The results suggest that non-local effects, reducing the maximum stress, become more pronounced with increasing geometric discontinuity quantified by the aspect ratio of ellipse which also influences equivalency between characteristic lengths of non-local models.

中文翻译：

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带有“隐式”和“显式”非局部模型的板中椭圆孔周围的应力分布

摘要 由于缺陷有意或无意地存在于许多材料中，因此了解缺陷的影响至关重要。经典的弹性理论可能不是描述结构行为的最佳候选者，因为它缺乏内部尺度参数，因此其潜在材料组织具有可比大小的缺陷。在这方面，目前的研究侧重于比较两种成熟的非本地理论；“隐式/弱”，如微极 (Cosserat) 和“显式/强”，如 Eringen 的，模型与经典模型的模型以突出它们在常见案例研究中的差异：无限板被不同纵横比的椭圆孔削弱，在远程单轴张力下。分数系数，提供与微极板相同的应力集中系数，搜索两阶段局部/非局部 Eringen 模型。结果是通过采用四边形单元的有限元方法获得的。为了说明域内的不连续性，通过使用大地距离而不是欧几里得距离来修改 Eringen 的模型，并且开发了计算上非常有效的程序来利用问题的对称特征而不会丢失远程交互。结果表明，减少最大应力的非局部效应随着由椭圆纵横比量化的几何不连续性的增加而变得更加明显，这也影响非局部模型的特征长度之间的等效性。Eringen 的模型是通过使用大地距离而不是欧几里得距离来修改的，并且开发了计算上非常有效的程序来利用问题的对称特征而不会丢失远程交互。结果表明，减少最大应力的非局部效应随着由椭圆纵横比量化的几何不连续性的增加而变得更加明显，这也影响非局部模型特征长度之间的等效性。Eringen 的模型是通过使用大地距离而不是欧几里得距离来修改的，并且开发了计算上非常有效的程序来利用问题的对称特征而不会丢失远程交互。结果表明，减少最大应力的非局部效应随着由椭圆纵横比量化的几何不连续性的增加而变得更加明显，这也影响非局部模型的特征长度之间的等效性。