TRANSIENT CONTACT INTERACTION OF A RIGID DIE AND ELASTIC HALF-SPACE WITH A CAVITY

A closed mathematical formulation of plane non-stationary contact problems for rigid dies and an elastic half-space with deepened cavities is constructed. Using the dynamic theorem of reciprocity of works, a system of resolving equations is obtained. It includes the basic boundary integral equation arising from the principle of reciprocity and boundary conditions, as well as the equations of translational and rotational motion of the die. The fundamental and singular solutions for the elastic plane are the cores of the main resolving equation. They determine displacements and stresses in the elastic plane from the applied single instantaneous concentrated force. An original solution algorithm based on the method of boundary integrals with an additional iterative procedure that allows one to take into account the partial separation of the boundary surfaces of the die and the half-space in the contact area has been developed and implemented on a computer. In this case, at each moment of time in the half-space, there is a region that is in a perturbed state and outside of which there are no perturbations. The integral operators of the resolving system of equations are replaced by discrete analogs in the spatial variable and in time. A parametric study of the process of unsteady contact of an absolutely rigid rectangular die with a half-space having a recessed cavity is carried out. Analysis of the calculation results revealed the manifestation of a significant effect of the cavity on the process of non-stationary contact interaction. The influence of the cavity begins to show itself from the moment the reflected waves arrive from its boundary. In this case, the nature of the unsteady stress-strain state and displacements changes significantly. The developed calculation algorithm can be used in engineering practice by design and research organizations in the process of designing and calculating buildings and structures under the influence of natural and man-made vibrations propagating in the soil.

Tribological Rehydration and Its Role on Frictional Behavior of PVA/GO Hydrogels for Cartilage Replacement Under Migrating and Stationary Contact Conditions

Graphene oxide (GO) was incorporated into polyvinyl alcohol (PVA) hydrogel to improve its mechanical and tribological performances for potential articular cartilage replacement application. The compressive mechanical properties, creep resistance, and dynamic mechanical properties of PVA/GO hydrogels with varied GO content were studied. The frictional behavior of PVA/GO hydrogels under stationary and migrating contact configurations during reciprocal and unidirectional sliding movements were investigated. The effects of load, sliding speed, diameter of counterface, and counterface materials on the frictional coefficient of PVA/GO hydrogels were discussed. PVA/0.10wt%GO hydrogel show higher compressive modulus and creep resistance, but moderate friction coefficient. The friction coefficient of PVA/GO hydrogel under stationary and migratory contact configurations greatly depends on interstitial fluid pressurization and tribological rehydration. The friction behavior of PVA/GO hydrogels shows load, speed, and counterface diameter dependence similar to those observed in natural articular cartilage. A low friction coefficient (~ 0.03) was obtained from PVA/0.10wt%GO hydrogel natural cartilage counter pair. Graphical Abstract

THE EFFECT OF PRESSURE AND TIME OF STATIONARY CONTACT UNDER LOAD ON THE STATIC FRICTION COEFFICIENT OF POLYURETHANE ELASTOMERS (EPUR) DURING FRICTION ON STEEL IN VARIOUS LUBRICATING CONDITIONS

Tribological tests were aimed at determining the value of static friction coefficient μ0 of EPUR with hardnesses 75, 80, 83, and 93 ° Sh A, during friction on C45 steel under various lubrication conditions. In the tests, the unit pressure values in the range of p = 0.2 – 0.8 MPa and the time of stationary contact under load were changed in the range of t = 1 – 9 min, both in dry friction conditions, lubricating with water, and lubricating with two types of greases – with low and high adhesion to steel. The tests were carried out on a device whose operating principle is based on an inclined plane. The results of the tests showed that both the unit pressure and the stationary contact time have a significant impact on the value of the static friction coefficient in the EPUR-steel pair.

Compressible Fluid Flow Simulation Using Finite Difference Lattice Boltzmann Method

A finite difference lattice Boltzmann method (FDLBM) is employed to simulate the compressible inviscid/viscous flows. The robustness of the employed approach is tested for the shock tube or Riemann problem in some distinct cases including strong pressure shock, the stationary contact discontinuity and the weak acoustic wave. The Results are compared with the exact solutions, as well as other classical finite volume CFD techniques (Steger-Warming, Roe and AUSM flux). The validity of the employed LBM approach is studied. This research reveals some of the challenges involved in simulating the compressible flows using FDLBM.