Multi-layer models for moving contact problems of graded materials and multiferroics

Toktaş, Selim Ercihan
In the present work, a solution method for the elastodynamic contact problems of rigid punches is developed for several smart systems in two dimensional medium. The considered composite structures always comprise a homogeneneous elastic substrate covered by a coating involving single layer or many sub-layers. The wear resistant coatings encountered in the industry possess heterogeneous structure and their properties are defined by gradation functions. Analytical contact solutions of such coatings generally focus on a single layer coating with exponential gradation through the depth of the coating as it is easier to work with the exponential function in the solution of differential equations. Yet, this assumption lacks in reality due to its limitations since the gradation function can be any function. The mathematical challenges of the random gradation functions are overcome by the discretization of the coating with homogeneous multi-layer modelling (HMLM) method. After homogenization of the structure, the formulation is based on the wave equations of plane elastodynamics and Maxwell’s equations depending on the coating type. By examining each layer with its own boundary conditions and applying Galilean and Fourier Transform techniques, the singular integral equation of the contact problem is derived for four different punches. In the next step, this equation is numerically solved by Jacobi expansion-collocation method to obtain the outputs. The main emphasize is the investigation of the influences of the coating type, the speed of the punch, the coating thickness-to-contact length ratio and the coefficient of dynamic friction on contact stresses, electric displacement and magnetic induction.
Citation Formats
S. E. Toktaş, “Multi-layer models for moving contact problems of graded materials and multiferroics,” Ph.D. - Doctoral Program, Middle East Technical University, 2024.