Multi-method examination of contact mechanics in orthotropic layers under gravity

Analyzing the behavior of intelligent unconventional materials under diverse contact scenarios, in comparison to conventional materials, is a critical step in the initial design of engineering systems. This paper presents the development of analytical and numerical approaches for analyzing contact mechanics in a system comprising an orthotropic layer resting on a rigid foundation. Parametric analyses include the consideration of cylindrical and flat punch profiles. Analytical formulation utilizes integral transform methods to convert planar elasticity equations into a Cauchy-type singular integral equation of the second kind. A detailed description of the solution technique for the integral equation is provided, encompassing both the analytical formulation and the required discretization for obtaining the solution. Subsequently, a finite element approach (FEA) is employed to approximate contact bodies using a collection of finite elements, while contact boundaries are approximated by utilizing a set of polygons. Alternatively, the problem is addressed using the Multilayer Perceptron approach, a form of artificial neural network frequently applied in diverse machine learning applications, including scenarios involving contact problems. Finally, the resolution to the problem is achieved by employing the multilayer perceptron (MLP) method. The study yields determinations of contact stresses under the punch, the critical separation load resulting in the detachment of the orthotropic layer from the rigid foundation, and the corresponding separation distance. This analysis considers a range of dimensionless parameters and explored the behavior of diverse orthotropic materials. Comparisons between the results of the analytical method and computations from FEA and MLP reveal the exceptional accuracy attained by all three approaches. As the pioneer study employing three distinct approaches to examine continuous contact mechanics within an orthotropic layer under the influence of gravity, this research constitutes a valuable point of reference for upcoming scholars in the field.