Ефективна пластична поведінка пористих матеріалів зі структурою інверсного опалу

Abstract

Based on the theoretical principles of the mechanics of composites, the effective plastic behavior of a porous material with a periodic inverse opal structure under uniaxial loading was studied in detail by means of finite element modeling. The creation of such materials is based on the inversion of pores and skeleton of partially sintered dense packing of polystyrene spheres. Electrodeposited nickel was used as the skeleton of the porous material. According to the macroscopic uniaxial loading or unloading, was finding a stress-strain state at the meso-level. For this, equilibrium equations were solved at the meso-level using special boundary conditions for a periodic unit cell. Such boundary conditions relate the problem of equilibrium at the meso-level with the "effective" deformations of the composite. This made it possible to calculate macroscopic residual strains after a cycle of uniaxial loading and unloading and iteratively find the value of effective stress corresponding to residual strains of 0.2%. In this way, the yield strength of inverse opal for uniaxial loading is calculated. At the same time, as a result of finite-element calculations, the transverse deformations coefficient (plastic Poisson ratio) is determined. This coefficient, in turn, makes it possible to approximate the general plastic behavior of the metamaterial by an elliptic yield curve in the plane of invariants of the stress tensor. Invariants mean average pressure and von Mises stress. These calculations were performing for several cases of the inverse opal structure, both with and without an additional coating. Yield stresses under any type of material loading are very sensitive to porosity. In particular, the application of an additional coating, even with a thickness less than 0,05 of the diameter of the spherical pores (initial polymer particles), causes an increase in the yield strength several times. Keywords: metamaterials, inverse opal, porous plasticity model, micromechanics, theory of plasticity.