Notes on the nonlinearly elastic Boussinesq problem (Q1338456)

We derive the governing equations from the principle of stationary potential energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half-space. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized new-Hookean (power-law) material and a compressible Blatz-Ko material.