Abstract
The indentation of a rectangular nonlinear hyperelastic membrane by a rigid paraboloid is presented in this paper. The strain-energy-density function for the membrane is assumed to have the Mooney form. The total potential energy of the deformed membrane can be obtained by integration. Due to the presence of a rigid indentor, the total potential energy for a deformed membrane is subjected to an inequality constraint condition. A slack variable is introduced to convert the inequality constraint condition into an equality constraint condition. Furthermore, a substitutional method is used to eliminate one of the unknown variables. In order to solve for the remaining unknown variables, the Raleigh-Ritz method and the minimum potential energy principle are employed. The deformations of a square membrane under various degrees of indentation are presented.
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