Application of the Finite Element Method to Modeling the Effective Mechanical and Thermomechanical Properties of Metamaterials of the 3D Lattice Structureтезисы доклада
Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
Аннотация:Metamaterials are composite materials, the properties of which are determined primarily by their
geometric microstructure, and not by the properties of the components included in their composition.
Such materials have a cellular structure and are manufactured using a 3D printer. The report describes
an approach to a numerical estimation of effective (averaged) properties of metamaterials, based on
the calculations on the periodicity cell of the material. Two types of metamaterials were studied. The
first kind is metamaterials with negative Poisson's ratio (NPR), which when stretched in one direction
expand in the other two. Such materials are used in medicine (stenting), in the manufacture of "smart"
filters, to increase the strength of structures experiencing shock loads, in the manufacture of protective
and damping materials. For NPR metamaterials, a numerical estimation of effective elastic properties
was carried out - in particular, Poisson's ratios. Six boundary value problems of the elasticity theory
with various periodic boundary conditions were solved at the periodicity cell of the material. Each
problem corresponds to the particular case of effective strain tensor of a cell: three uniaxial tensions
and three shear deformations. Distributions of stress tensors obtained as a result of solving problems
were averaged over the volume. Effective elastic properties were estimated as a relation between the
stress tensor and the strain tensor.
We studied a dependence of the effective Poisson's ratios on the geometric parameters of the
metamaterial cell. The parameters of cells, in which the Poisson's ratio comes to -1, were found. In
addition, metamaterials with a negative thermal expansion coefficient (NTE), which shrink when
heated, were studied. Such structures are made of two components: a harder one with a smaller
thermal expansion coefficient and a softer one with a larger coefficient. To be precise, the materials
that, when heated and cooling, do not change their sizes are of practical interest. They can be used in
microchip devices, adhesive fillings, dental fillings and high-precision optical or mechanical devices
in environments with varying temperatures. For NTE metamaterials, a numerical estimation of the
effective thermal expansion coefficients was carried out. We solved the boundary value problem of
thermoelasticity on a periodicity cell with a given heating value and periodic boundary conditions,
allowing the cell to deform arbitrarily strongly, while remaining a periodicity cell. The strain tensor
field, obtained as a result of solving the problem, was averaged over the volume. The effective thermal
expansion was estimated in the form of a linear dependence of the effective deformation tensor on the
heating value of the cell. We studied the dependence of the effective thermal expansion coefficients on
the geometric parameters of the metamaterial cell. The parameters of the cells, under which the
effective thermal expansion coefficient is negative and maximized by the module, are found - as well
as the parameters under which it is almost equal to zero. Calculations of the cell stability were
performed with the obtained parameters to thermal deformation for deeper analysis. The calculations
of effective properties were carried out using the Fidesys Composite software module of CAE Fidesys.
The report presents the results of calculations in the form of graphs of dependences of effective
properties on the geometric parameters of the cell. The work was supported by the Russian President's
grant for young scientists - Ph.Ds MD-208.2021.1.1.