Analysis of the tilted flat punch in couple-stress elasticity

Abstract

Abstract. In the present paper we explore the response of a half-plane indented by a tilted flat punch with sharp corners in the context of couple-stress elasticity theory. Contact conditions arise in a number of modern engineering applications ranging from structural and geotechnical engineering to micro and nanotechnology. As the contact scales reduce progressively the effects of the microstructure upon the macroscopic material response cannot be ignored. The generalized continuum theory of couple-stress elasticity introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying material microstructure. The problem under investigation is interesting for three reasons: Firstly, the indentor's geometry is simple so that benchmark results may be extracted. Secondly, important deterioration of the macroscopic results may emerge in the case that a tilting moment is applied on the indentor inadvertently or in the case that the flat punch itself is not self-aligning so that asymmetrical contact pressure distributions arise on the contact faces. Thirdly, the voluntary application of a tilting moment on the flat punch during an experiment gives rise to potential capabilities of the flat punch for the determination of the material microstructural characteristic lengths. The solution methodology is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that valuable information may be deducted from the indentation of a tilted punch of a microstructured solid.

Elastohydrodynamic lubrication line contact in couple-stress elasticity

“…The results showed that characteristic material length was a significant influencing factor on the contact behaviors of microstructured materials. A similar problem was later investigated by Gourgiotis and Zisis [22] for a wedge punch and a cylindrical punch and by Gourgiotis et al [23] for a tilted flat punch. Applying the Fourier integral transform and the generalized stress function method and considering the influence of heat flux, steady-state thermomechanical contact of a smooth flat punch was investigated by considering the influence of the couple stress [24].…”

“…Referring to [8,23], the constitutive equations can be written as…”

Identification of second-gradient elastic materials from planar hexagonal lattices. Part I: Analytical derivation of equivalent constitutive tensors

“…Recently, experimental observations at the micro-and nano-scale have evidenced size-effects [9,12,22,37], which cannot be described with local constitutive models. Therefore, an enhanced modelling has been introduced, which becomes particularly useful when large strain gradient are involved, as in contact mechanics [19,38] indentation processes [8,15], fracture [18,28], and shear band formation [14,32].…”

Shear crack growth in brittle materials modeled by constrained Cosserat elasticity

“…For the isotropic case, the constrained Cosserat theory introduces material length scales which can be related to the intrinsic material microstructure [21,22,23,24]. The constrained Cosserat theory has been recently employed successfully to model size effects in microstructured materials in, among other areas, fracture [25,26,27,28,29,30,31], contact [32,33,34], stress localization [35,36,37,38], and wave propagation problems [39,40,41,42].…”