title: A mathematical approximation for the solution of a static indentation test.
abstract: The classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered. Closed-form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane-ended (axisymmetric) cylinder. The approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution. In the case of plane indentation, the mathematical and classical predictions agree to within 2% relative error for aspect ratios between 0.1 and 1.0 and apparent Poisson ratio between 0.0 and 0.3. Comparisons for the axisymmetric case indicate a similar pattern. The main advantage of the new approach is that it yields closed-form approximations of the static indentation solution which can also capture the essential singular behavior.
authors.affiliation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.
authors.forename: M A
authors.initials: MA
authors.lastname: Haider
authors.forename: M H
authors.initials: MH
authors.lastname: Holmes
mesh_terms: D000818:Animals; D002358:Cartilage, Articular / Q000502:physiology; D019245:Compressive Strength / Q000502:physiology*; D004548:Elasticity; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D011312:Pressure; D013314:Stress, Mechanical; D013499:Surface Properties