Axisymmetric indentation of an elastic thin plate by a rigid sphere revisited. Issue 8 (2nd May 2018)

• Record Type: Journal Article
• Authors: Li, Min; Ru, C.Q.; Gao, Cun‐Fa
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 98:Issue 8(2018)
• Page Start: 1436
• Page End: 1446
• Publication Date: 2018-05-02
• Subjects: contact -- indentation -- indenter -- Kerr model -- plate; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201700266
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: A simple analytical model based on a Kerr‐type differential relation is proposed to study the indentation problem of a circular elastic thin plate indented by a rigid sphere. Unlike some existing methods which matched two solutions inside and outside the contact zone, the present method is based on a simple differential relation between contact pressure and the normal deflection of the pressured surface of elastic plate, which holds both inside and outside the contact zone and makes it possible to analyze both zones by a single governing differential equation. Explicit relations between the contact‐zone radius, indentation displacement and indentation load are derived for different boundary conditions. The proposed model is validated by good agreement between the predicted results and some known data available in existing literature. In particular, the present model confirms that the indenter will lose contact with the plate around the center of the plate as the indentation load exceeds a certain critical value, and then the contact zone becomes to an annular zone. Detailed analytical and numerical results beyond existing literature are demonstrated for the annular contact zone regarding the critical contact‐zone radius, the width of annular contact zone and the associated contact pressure distribution. Abstract : A simple analytical model based on a Kerr‐type differential relation is proposed to study the indentation problem of a circular elastic thin plate indented by a rigid sphere. Unlike some existing methods which matched two solutions inside and outside the contact zone, the present method is based on a simple differential relation between contact pressure and the normal deflection of the pressured surface of elastic plate, which holds both inside and outside the contact zone and makes it possible to analyze both zones by a single governing differential equation. Explicit relations between the contact‐zone radius, indentation displacement and indentation load are derived for different boundary conditions. The proposed model is validated by good agreement between the predicted results and some known data available in existing literature.…