2D analytical method for the interface stress transfer in a graphene monolayer nanocomposite

研究目标如下：在简化假设、边界和接触条件下，简化石墨烯纳米复合材料代表性体积元（RVE）的二维弹性问题。推导和求解了第一层纵向应力的四阶常微分方程，并将RVE中所有应力表示为一阶导数和二阶导数的函数。在适当的判据下，将发现并详细讨论界面分层。本研究将在石墨烯/聚合物纳米复合材料具有有限厚度的代表性体积各向同性弹性元件的二维线性简化模型框架下进行。结构受拉伸应变（应力）的作用。选择二维简化方法作为分析工具是基于其对单搭接不同问题的众所周知的优势。虽然该方法已经在该领域获得批准，但其进一步发展和扩展将伴随着石墨烯薄片嵌入PMMA基体的使用，这可以提高所考虑的纳米复合材料的强度和韧性。因此，改变基板的机械性能以及结构的机械载荷和几何形状，可以避免可能的界面分层。对于这类问题，申请者迄今积累的经验是克服上述计算问题的保证。

The research objectives can be summarized as follows:Reduction of 2D elastic problem for a representative volume element (RVE) of a graphene nanocomposite under simplifying assumptions and boundary and contact conditions. Derivation and solution of 4th order ordinary differential equation about longitudinal stress in the first layer and presentation of all stresses in RVE as functions of its first and second derivatives. Under proper criterion the interface delamination will be found and discussed in detail. Research and computational methodology The proposed research will be done in the frame of a 2D-dimensional linear reduced model for the graphene/polymer nanocomposite representative volume isotropic elastic element with a finite thickness. The structure is loaded by a tensile strain (stress). The choice of the 2D reduced method as an analytical tool is based on its well-known advantages for different problems in single lap joint. Although the method is already approved in this field, its further development and extension will go along with a use of graphene flake embedded in PMMA matrix, which can increase the strength and toughness of considered nanocomposite. Thus, varying the mechanical properties of the substrate as well as the mechanical loading and geometry of the structure, the possible interface delamination may be avoided. The hitherto accumulated experience by the applicants for these kinds of problems is a guarantee for overcoming the computational problems discussed above.