Construction of the simplified analytical solution of the flat punch indentation contact problem

The paper is devoted to the construction of the approximated solution for the flat-ended circular punch indentation contact problem for an elastic isotropic half-space with a coating. We assume the coating to be either homogeneous (elastic moduli are constant) or functionally graded (elastic moduli vary by depth). The solution of the problem is constructed using the bilateral asymptotic method. One-parameter approximation of the kernel transform of the integral equation is used to obtain explicit analytical expressions for the contact stresses distribution as well as the load-displacement dependence in a simplified form, which is convenient for engineering calculations. The accuracy analysis of the obtained solution is carried out on example of a series of homogeneous and functionally graded coatings. The influence of a parameter characterizing the relative Young’s modulus of the coating and the law of variation of Young’s modulus in depth on the accuracy of the simplified is analyzed.The paper is devoted to the construction of the approximated solution for the flat-ended circular punch indentation contact problem for an elastic isotropic half-space with a coating. We assume the coating to be either homogeneous (elastic moduli are constant) or functionally graded (elastic moduli vary by depth). The solution of the problem is constructed using the bilateral asymptotic method. One-parameter approximation of the kernel transform of the integral equation is used to obtain explicit analytical expressions for the contact stresses distribution as well as the load-displacement dependence in a simplified form, which is convenient for engineering calculations. The accuracy analysis of the obtained solution is carried out on example of a series of homogeneous and functionally graded coatings. The influence of a parameter characterizing the relative Young’s modulus of the coating and the law of variation of Young’s modulus in depth on the accuracy of the simplified is analyzed.