Impact indentation of a rigid body into an elastic layer. Analytical and numerical approaches

Анотація

A plane contact-impact problem is considered for an elastic layer subjected to indentation of a rigid body moving with a given velocity. An exact analytical solution is obtained in the case of a blunt contour of the indenter shape. Results of the solution are presented for stresses developed with time in a layer of a finite thickness. Stress pattern under multiple reflections is analyzed. A numerical solution of the problem is obtained on the basis of the simplified model of the elasticity theory having a single displacement. The explicit finite difference algorithm is developed on the basis of the mesh dispersion minimization technique resulting in precise calculations of discontinuities. Calculated stresses and force of resistance to pressing are presented in the cases of irregular shapes of the indenter contour (rectangle, wedge and their combination).