Modern advances in material science and surface chemistry lead to creation of composite materials with enhanced mechanical, thermal, and other properties. It is now widely accepted that the enhancements are achieved due to drastic reduction in sizes of some phases of composite structures. This leads to increase in surface to volume ratios, which makes surface-or interface-related effects to be more significant. For better understanding of these phenomena, the investigators turned their attention to various theories of material surfaces. This paper is a review of two most prominent theories of that kind, the Gurtin-Murdoch and Steigmann-Ogden theories. Here, we provide comprehensive review of relevant literature, summarize the current state of knowledge, and present several new results.
Bibliographical noteFunding Information:
• Isaac Newton Institute for Mathematical Sciences (Grant No. EP/R014604/1; Funder ID: 10.13039/501100005347).
The first author (S.M.) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. The second author (A.Z.) gratefully acknowledges the support from the Simons Foundation under the Simons Collaboration Grant for Mathematicians, project 713080. The first and second authors (S.M. and A.Z.) gratefully acknowledge support of the Isaac Newton Institute for Mathematical Sciences (INI) at Cambridge University, which enabled their participation in the INI programme on “Complex analysis: techniques, applications and computations” (EPSRC grant EP/R014604/1) In this context, the first author (S.M.) also gratefully acknowledges the support of the Simons Foundation through a Simons INI Fellowship. Special thanks to Dr. Z. Han and Ms. S. Baranova for the help with preparation of this paper.
© 2021 by ASME.
- Fiber-and particle-reinforced composites
- Gurtin-Murdoch and Steigmann-Ogden theories
- local and overall behavior
- surface energy