Abstract:
An asymptotic solution of the contact problem of an elastic body indented (without friction) by a circular punch with a flat base is obtained under the assumption of a small relative size of the contact zone. The resulting formulas involve integral characteristics of the elastic body, which depend on its shape, dimensions, fixing conditions, Poisson's ratio, and location of the punch center. These quantities have the mechanical meaning of the coefficients of local compliance of the elastic body. Relations that, generally, reduce the number of independent coefficients in the asymptotic expansion are obtained on the basis of the reciprocal theorem. Some coefficients of local compliance at the center of an elastic hemisphere are calculated numerically. The asymptotic model of an elastic body loaded by a point force is discussed.
Citation:
I. I. Argatov, “Characteristics of local compliance of an elastic body under a small punch indented into the plane part of its boundary”, Prikl. Mekh. Tekh. Fiz., 43:1 (2002), 177–185; J. Appl. Mech. Tech. Phys., 43:1 (2002), 147–153
\Bibitem{Arg02}
\by I.~I.~Argatov
\paper Characteristics of local compliance of an elastic body under a small punch indented into the plane part of its boundary
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2002
\vol 43
\issue 1
\pages 177--185
\mathnet{http://mi.mathnet.ru/pmtf2595}
\elib{https://elibrary.ru/item.asp?id=17274635}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2002
\vol 43
\issue 1
\pages 147--153
\crossref{https://doi.org/10.1023/A:1013986800740}
Linking options:
https://www.mathnet.ru/eng/pmtf2595
https://www.mathnet.ru/eng/pmtf/v43/i1/p177
This publication is cited in the following 8 articles:
Ivan Argatov, Valentin L. Popov, “An adhesive detachment paradox: Does the substrate thickness matter?”, Mechanics Research Communications, 129 (2023), 104093
Ivan Argatov, “On the Sevostianov–Kachanov approximation for the incremental compliances of non-elliptical contacts”, Mathematics and Mechanics of Solids, 2022, 108128652211221
I. I. Argatov, “An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness”, Math Methods in App Sciences, 41:2 (2018), 495
I I Argatov, F M Borodich, V L Popov, “JKR adhesive contact for a transversely isotropic layer of finite thickness”, J. Phys. D: Appl. Phys., 49:4 (2016), 045307
Ivan I. Argatov, Federico J. Sabina, “Small-scale indentation of a hemispherical inhomogeneity in an elastic half-space”, European Journal of Mechanics - A/Solids, 53 (2015), 151
I. Argatov, A.U. Daniels, G. Mishuris, S. Ronken, D. Wirz, “Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: Application to non-destructive testing of articular cartilage”, European Journal of Mechanics - A/Solids, 37 (2013), 304
Ivan I. Argatov, Raúl Guinovart-Díaz, Federico J. Sabina, “On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint”, International Journal of Engineering Science, 54 (2012), 42
I. Argatov, “Frictionless and adhesive nanoindentation: Asymptotic modeling of size effects”, Mechanics of Materials, 42:8 (2010), 807
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