Material design of anisotropic elastic cellular bodies with respect to contact problem

Two-dimensional contact problem formulated for anisotropic, elastic bodies is considered.
As an example of anisotropic medium, the cellular material is taken. The idea of two-scale
modeling is adopted for formulation of an equivalent continuum, on the basis of which elastic
properties can be obtained [2, 3]. Typical cellular microstructures with various types of symme-
tries are considered. Special attention is paid to cell structures giving negative Poisson’s ratio
in some directions (re-entrant cells). Application of the energy-based criterion for equivalent
continuum gives macroscopic yield condition [2, 5]. Condition for the energy coefficient defined
as a sum of weighted energies stored in elastic eigenstates ensures that the material works in
elastic state. Unilateral frictional contact problem is analyzed using FEM. Calculations are
performed for rough contact of square block subjected to normal load. Numerical solutions
show differences in deformation type and contact stress distributions for different types of
microstructures of the analyzed medium. The study enables the optimal choice of material
structure topology, which ensures the reduction of peak contact pressure and friction stress,
and applicability of anisotropic material to the given problem.