CALCULATION MODELS FOR STATIC ANALYSIS OF THREE-DIMENSIONAL NANOCOMPOSITES WITH SYSTEMS OF INCLUSIONS
DOI:
https://doi.org/10.32782/2618-0340/2019.2-2.3Keywords:
three-dimensional composites and nanocomposites, interface surfaces, classical and non-classical contact conditions, finite and boundary element methodsAbstract
Approach based on the principles of continuum mechanics is used to estimate the mechanical properties of three-dimensional composites and nanocomposites. Mechanical properties of composites and nanocomposites are considered in the assumptions of linear elasticity. To describe the nanoscale contact between matrices and inclusions on the interface surface, the conditions of ideal contact and non-classical Gurtin-Murdoch conditions are used. The interface surface is regarded as an elastic membrane with its own elastic characteristics and a given surface tension. The special algorithm for numerical solution of resolving equations is developed when the integration area is a surface of rotation. In this case, static problems of determining the elastic characteristics of nanocomposites are reduced to systems of one-dimensional singular integral equations. Different types of representative volume elements are considered. Finite and boundary element methods are used in numerical estimation of the mechanical properties of composite and nanocomposite materials. For the three-dimensional problem, the results obtained using the finite element method (hexagonal representative volume element) and the boundary element method (cylindrical representative volume element) are compared. The finite element method is used to find out the stress-strain state of various representative volume elements of threedimensional nanocomposites. The influence of shapes and relative sizes of inhomogeneities and matrices of representative volumes on the effective elasticity modulus of nanocomposites is studied. Matrices in the form of cube and cylinder of finite sizes and inhomogeneity in the form of balls, spheres, cylinders, fibers and tubes are considered. Finite element-based calculation models are generalized to composites with distributed nanoinclusions of random and ordered orientation. The resulting models create an informative base for nanocomposites synthesis technologies with improved deformable and strength characteristics.
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