TY - JOUR
T1 - Depth-sensing spherical indentation of an elastic sphere on an elastic substrate
AU - Argatov, Ivan I.
AU - Jin, Xiaoqing
AU - Keer, Leon M.
N1 - Funding Information:
This work is supported by the National Science Foundation of China (Grant Nos. 11932004 and 51875059 ). X.J. would like to acknowledge the support from Chongqing City Science and Technology Program (Grant No. cstc2020jcyj-msxmX0850 ). I.A. is grateful to the financial support from the Ba-Yu Scholar program of Chongqing City (China) . The authors would like to express their gratitude to the Referees for their careful reading and valuable comments.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/4
Y1 - 2021/4
N2 - The axisymmetric three-body, double-unilateral contact problem for an elastic sphere is treated by analytical techniques. It is assumed that the elastic sphere is put on the surface of an elastic layer of finite thickness and, afterwards, is indented at the upper pole of the sphere with a rigid spherical punch. Friction is neglected at both contact interfaces. A first-order asymptotic solution for the displacement–force relation, which generalizes the corresponding Hertzian formula, is derived in explicit form in terms of dimensionless asymptotic constants that account for the finite sizes of the elastic sphere and layer. Under the assumption that the sphere/substrate contact diameter is less than the substrate thickness, the presented results can cover a wide range of parameter combinations, which may be used for the purpose of benchmark assessments in the finite element analysis. The constructed asymptotic model is remarkably simple and elegant, and yet can be applied to various contact problems of practical importance (including a very timely problem of indentation of spherical viruses). The underlying theoretical framework is versatile and can be further extended for analysis of multiple contacts involving elastic spheres and elastic layers.
AB - The axisymmetric three-body, double-unilateral contact problem for an elastic sphere is treated by analytical techniques. It is assumed that the elastic sphere is put on the surface of an elastic layer of finite thickness and, afterwards, is indented at the upper pole of the sphere with a rigid spherical punch. Friction is neglected at both contact interfaces. A first-order asymptotic solution for the displacement–force relation, which generalizes the corresponding Hertzian formula, is derived in explicit form in terms of dimensionless asymptotic constants that account for the finite sizes of the elastic sphere and layer. Under the assumption that the sphere/substrate contact diameter is less than the substrate thickness, the presented results can cover a wide range of parameter combinations, which may be used for the purpose of benchmark assessments in the finite element analysis. The constructed asymptotic model is remarkably simple and elegant, and yet can be applied to various contact problems of practical importance (including a very timely problem of indentation of spherical viruses). The underlying theoretical framework is versatile and can be further extended for analysis of multiple contacts involving elastic spheres and elastic layers.
KW - Asymptotic modeling
KW - Depth-sensing indentation
KW - Elastic sphere
KW - Indentation compliance
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U2 - 10.1016/j.jmps.2021.104297
DO - 10.1016/j.jmps.2021.104297
M3 - Article
AN - SCOPUS:85100381945
SN - 0022-5096
VL - 149
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
M1 - 104297
ER -