Concentrated force acting on a power law creep half-plane

The problem of concentrated force acting on a half-plane made of a power-law creep material is solved analytically. In our approach, the constitutive equation that describes the process of dilatational deformation is omitted. The incomplete material description is used for constructing a solution by bringing the dilatational deformation to zero and, in this manner, making the material incompressible. We find solutions for two cases; one solution is for a linear viscous material, while the second is for a power-law material where the power exponent is equal to three. Solutions of the two problems are found to be very different. While the linear viscous solution is found to be the same as the linear elastic solution, the nonlinear solution is found to be significantly different. This result may give rise to a new experimental technique for characterization of materials with a nonlinear creep behavior.