Indentation of a Membrane on an Elastic Half Space

Abstract

An analysis is presented of the deformation of a homogeneous isotropic elastic half space whose surface behavior departs from the classical due to the presence of a pretensed membrane or a material surface which exhibits surface tension. Two related problems are considered: the axisymmetric displacements caused by a uniform circular load and by a concentrated normal force. In contrast to the classical solution, the uniform load problem with surface tension is found to have a finite slope and zero shear stress over the entire boundary. The analysis is used to interpret data from indentation tests on inflated dog lobes and the mechanical properties of both the lung parenchyma and the surface membrane are obtained. The observed shape of the indented surface agrees well with the prediction of the analysis.