Punch problem for initially stressed neo-Hookean solids

The paper reports the indentation of a semi-infinite, initially stressed elastic medium under the action of an axisymmetric rigid punch pressing the medium normally The problem has been considered within the framework of incremental deformation theory for neo-Hookean solids. Using the Hankel's transformation, the distributions of incremental stress and strain have been obtained. Indentations by a flat-ended circular cylindrical punch and a conical punch have been obtained as special cases and these effects have been studied numerically and presented in the form of curves. This problem has defence application as many launching pads and firing machines have some neo-Hookean solids as buffer which bear enormous impact or punch during the action of the machine.