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Two-dimensional indentation of microstructured solids characterized by couple-stress elasticity

In this study, we derive general solutions for two-dimensional plane strain contact problems within the framework of the generalized continuum theory of couple-stress elasticity. This theory introduces characteristic material lengths and is able to capture the associated scale effects that emerge from the material microstructure which are often observed in indentation tests used for the material characterization. The contact problems are formulated in terms of singular integral equations using a Green’s function approach. The pertinent Green’s function obtained through the use of integral transforms corresponds to the solution of the two-dimensional Flamant–Boussinesq half-plane problem in couple-stress elasticity. The results show a strong dependence on the microstructural characteristics of the material when this becomes comparable to the characteristic dimension of the problem, which in the case of an indentation test is the contact length/area.