The use of the Gurtin-Murdoch theory for modeling mechanical processes in composites with two-dimensional reinforcements. (7th July 2021)

• Record Type: Journal Article
• Authors: Mogilevskaya, Sofia G.; Zemlyanova, Anna Y.; Mantič, Vladislav
• Is Part Of: Composites science and technology. Volume 210(2021)
• Publication Date: 2021-07-07
• Subjects: Nano composites -- Graphene and other 2D-materials -- Elastic behavior -- Stress transfer -- Gurtin-Murdoch theory; Composite materials -- Periodicals; Composite materials; Fibrous composites; Periodicals; 620.118
• DOI: 10.1016/j.compscitech.2021.108751
• Languages: English
• ISSNs: 0266-3538

Abstract

Abstract: This paper explores the possibility of using the Gurtin-Murdoch theory of material surface for modeling mechanical processes in nanomaterials reinforced by two-dimensional flexible and extensible nanoplatelets. In accordance with the theory, reinforcement is modeled by a vanishing thickness prestressed membrane embedded in an isotropic elastic matrix material. The governing equations for the model are reviewed with a detailed discussion of the conditions at the membrane tips. Plane strain assumption is made and with the purpose of representing the displacements in the bulk material, a single layer elastic potential is employed, with the density representing the jump in tractions across the membrane. Expressions for the remaining elastic fields are provided in terms of complex integral representations. The case of a rectilinear membrane of finite length is considered in detail. Numerical solution for this case is based on the use of approximations that automatically incorporate the membrane-tip conditions into the resulting system of boundary integral equations. Numerical examples illustrate the influence of governing dimensionless parameters and present simulations of the local elastic fields in the materials under study. Additionally, it is shown that, in absence of surface tension, the problem considered here is related to that of a membrane type elastic inhomogeneity embedded into a homogeneous elastic medium. Graphical abstract: Image 1