Total Deformation, Plane-Strain Contact Analysis of Macroscopically Homogeneous, Compositionally Graded Materials With Constant Power-Law Strain Hardening

Plane-strain contact analysis is presented for compositionally graded materials with power-law strain hardening. The half-space, $y≤0$⁠, is modeled as an incompressible, nonlinear elastic material. The effective stress, σ_e, and the effective total strain, ε_e, are related through a power-law model, $σe=K0εeμ;0<μ≤min(1,(1+k)$⁠). The material property K₀ changes with depth, $|y|$⁠, as $K0=A|y|k;A>0,0≤|k|<1$⁠. This material description attempts to capture some features of the plane-strain indentation of elastoplastic or steady-state creeping materials that show monotonically increasing or decreasing hardness with depth. The analysis starts with the solution for the normal line load (Flamant’s problem) and continues with the rigid, frictionless, flat-strip problem. Finally, the general solution of normal indentation of graded material by a convex, symmetric, rigid, and frictionless two-dimensional punch is given. Applications of the present results range from surface treatments of engineering structures, protective coatings for corrosion and fretting fatigue, settling of beam type foundations in the context of soil and rock mechanics, to bioengineering as well as structural applications such as contact of railroad tracks.