Nanocomposites and nanomaterials

Effective elastic properties of 3D nanocomposites reinforced by short-fiber with Gurtin-Murdoch model of interphase
Mykhas’kiv V. V.1, Stasyuk B. M.2
1Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU,
3-b Naukova Str., 79060 Lviv, Ukraine
2Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, Ukraine
E-mail: stasyuk.bohdan.m@gmail.com

Advances in nano-scale science and engineering is due to the development of interface elasticity models with tension effect. In Gurtin-Murdoch model [1] the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces with their own mechanical properties and surface tension. The interface stress effect at the nanoscale case has been modeled by many researchers using analytical or numerical methods [2-3]. 
This work contains solution of two associated subproblems. 
1. Numerical simulation of displacements and tractions on the inhomogeneity-matrix interfaces in the representative volume element based on the boundary element method. Gurtin-Murdoch contact conditions are considered explicitly in the obtained system of boundary integral equations, which further are regularized and discretized on the involved mesh of boundary elements. Inclusion has the form of finite cylindrical fiber with the rounded edges. 
2. Effective strain-stress field approximation by the homogenization procedures. As the averaging scheme, Mori-Tanaka model [4] is modified for the overall description of nanocomposite properties at the macro-level in the case where fibers are parallel or randomly distributed, and their interphase is assumed to be adequately described by the material surface model.
This work was supported by NANU-STCU (Project No. 6247) 

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