Adhesive impact of an elastic sphere with an elastic half space: Numerical analysis based on the method of dimensionality reduction

Method of Dimensionality Reduction in Contact Mechanics and Friction: A User's Handbook. Ii. Power-Law Graded Materials

“…The same applies to the extension of the current numerically simulated impact problems between elastically homogeneous spheres [21,22] onto elastically inhomogeneous ones. Based on the MDR-rules presented here, which are comprehensible to everyone, the development of asymptotic solutions [23] for complicated contact configurations between powerlaw graded materials is also likely to be much easier.…”

Tangential Displacement Influence on the Critical Normal Force of Adhesive Contact Breakage in Biological Systems

“…As a result, the force value is fixed during the relaxation process. We note that the MDR-relations described before have been successfully applied to the simulation of the adhesion influence at particles elastic collisions under "fixed-grips" loading conditions [17].…”

Influence of Tangential Displacement on the Adhesion Force between Gradient Materials

“…The controlled force condition is realized when the indenter is moved by means of a very soft spring, when the force value does not change at every contact relaxation to the equilibrium state (the soft spring can be stretched to a rather large size; therefore, small indenter displacements do not substantially affect the spring elongation and, hence, the effective force). Earlier, we have used the MDR to simulate the influence of the adhesive interaction on collisions between elastic spherical particles under the controlled displacement condition [19].…”

“…= 0. Attention should be paid to that expression (19) describes a situation where the work of the adhesive forces does not depend on the indenter motion direction. This assumption may be not valid for some physical systems [21,22].…”