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Multiple interacting circular nano-inhomogeneities with surface/interface effects. (English) Zbl 1171.74398
Summary: A two-dimensional problem of multiple interacting circular nano-inhomogeneities or/and nano-pores is considered. The analysis is based on the Gurtin and Murdoch model [M. E. Gurtin and A. I. Murdoch, Arch. Ration. Mech. Anal. 57, 291–323 (1975; Zbl 0326.73001)] in which the interfaces between the nano-inhomogeneities and the matrix are regarded as material surfaces that possess their own mechanical properties and surface tension. The precise component forms of Gurtin and Murdoch’s three-dimensional equations are derived for interfaces of arbitrary shape to provide a basis for critical review of various modifications used in the literature. The two-dimensional specification of these equations is considered and their representation in terms of complex variables is provided. A semi-analytical method is proposed to solve the problem. Solutions to several example problems are presented to: (i) examine the difference between the results obtained with the original and modified Gurtin and Murdoch’s equations, (ii) compare the results obtained using Gurtin and Murdoch’s model and those for a problem of nano-inhomogeneities with thin membrane-type interphase layers, and (iii) demonstrate the effectiveness of the approach in solving problems with multiple nano-inhomogeneities.

MSC:
74M25 Micromechanics of solids
74E05 Inhomogeneity in solid mechanics
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