COMPUTATIONAL MODELS FOR THE ANALYSIS OF MECHANICAL PROPERTIES OF THREE-DIMENSIONAL NANOCOMPOSITES BASED ON THE METHODS OF FINITE AND BOUNDARY ELEMENTS

Abstract

To study the local deformation and strength properties of nanocomposites with single inclusions or inhomogeneities, the boundary-element and finite-element formulations of threedimensional static problems of elasticity theory are performed. The finite element method is used to determine the stress-strain state of various representative volume elements of 3D nanocomposites. The main objective is to study the influence of forms and relative sizes of inhomogeneities and matrices for representative volumes on the elasticity effective modulus of nanocomposites. The matrixes in the form of a hexagonal prism and a finite-size cylinder are considered. Inhomogeneities are considered as spheres or cylinders with rounded edges. Using the method of boundary elements, the reduction of two-dimensional singular equations of the elasticity theory to one-dimensional ones has been made when the integration domain is a surface of rotation. The completeness of the system of boundary integral equations is achieved by considering the given differential connection between the displacement components and traction jump on the nanosized surface separated the materials. For the nanoinclusion zero-elastic characteristics, the system of key integral and differential equations is obtained on the nanohole surface in the three-dimensional elastic matrix for a static load. Finite-elemental formulation is made taking into account the conditions of full contact on nanoscale material separation surfaces. Then the static problems of determining the elastic characteristics of nanocomposites are reduced to solving systems of onedimensional singular integral equations. This allows us to develop only one procedure for determining the elastic characteristics that can be used to describe the elastic displacements and tractions in the matrix as well as in the inclusion. The calculations have proved that for estimation the effective module of elasticity of the nanocomposite it is sufficient to consider the matrix with single inclusion, since bulky, multi-matrix models do not show results that are different from the case of single inclusion.