Revisit of the two-dimensional indentation deformation of an elastic half-space

Recently, there is a growing interest in two-dimensional (2D) plane indentation as an imprinting method for creating nanostructures. There is also a strong interest in using 2D flat-ended, wedge, and cylindrical indenters for characterizing mechanical properties of materials. In either case the knowledge of load versus displacement of the indenter is important. However, there has been some confusion about the load-displacement relationships for 2D indentation in the literature. Concerning this confusion on the relationship between the indentation load and the indentation depth for 2D elastic indentations, the symmetric indentation of an elastic half-space is studied. Parameters are introduced in determining the semianalytical relation between the indentation load and the indentation depth for flat-ended indenters and in determining the dependence of the indentation depth on the contact size for non-flat-ended indenters. The indentation load is proportional to the indentation depth for the indentation by flat-ended indenters and is a parabolic function of the indentation depth to the first order of approximation for non-flat-ended indenters including the wedge and cylindrical indenters.