Three-Dimensional State with Doublet Mechanics

In this study, it is aimed to obtain general stress expressions for the examination of mechanical behaviors of planar straight axis nano rods by using doublet mechanics. The superiority of this method over other scale dependent methods is that it is directly related to the structure of nanomaterial and it models solid structure with points at finite distances between them. In other words, value of small scale effect is known exactly. To the best of authors’ knowledge, after micro modulus matrix is obtained by using Generalized Hooke’s Law and the essential transformation matrix expressing relationships between macro and micro stress and strain matrix, the stress equations that include the effect of axial extension are acquired for the three-dimensional state for the first time in the literature. In plane and out of plane static and dynamic behaviors can be studied using analytical and/or numerical approaches without any restrictions. Since the value of the small scale size parameter is precisely known in the theory used, it is thought that the results to be obtained will be more accurate than other scale size theories.

• Hilal Koç
• Ekrem Tüfekci

• axial extension
• doublet mechanics
• granular material
• three-dimensional state

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