Abstract: The Boussinesq problem, which describes quasi-static indentation of a rigid punch into a deformable body, is studied within the context of nonlinear constitutive equations. By this, the material response expresses the linearized strain in terms of the stress and cannot be inverted in general. A contact area between the punch and the body is unknown a priori, whereas the total contact force is prescribed and yields a non-local integral condition. Consequently, the unilateral indentation problem is stated as a quasi-variational inequality for unknown variables of displacement, stress and indentation depth. The Lagrange multiplier approach is applied in order to establish well-posedness to the underlying physically and geometrically nonlinear problem based on augmented penalty regularization and applying the minimax theorem of Ekeland and Témam. A sufficient solvability condition implies response functions that are bounded, hemi-continuous, coercive and obey a convex potential. A typical example is power-law hardening models for titanium alloys, Norton–Hoff and Ramberg–Osgood materials. This article is part of the theme issue ‘Non-smooth variational problems and applications’.

Cite: Kovtunenko V.A.
Quasi-variational inequality for the nonlinear indentation problem: a power-law hardening model
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022. V.380. N2236. 20210362 . DOI: 10.1098/rsta.2021.0362 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Oct 26, 2021
Accepted:	Dec 20, 2021
Published print:	Sep 26, 2022

Identifiers:

Web of science:	WOS:000861201200007
Scopus:	2-s2.0-85138536289
Elibrary:	56653023
OpenAlex:	W4297143780

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Scopus	4
OpenAlex	7
Web of science	7

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