Fiber- and Particle-Reinforced Composite Materials With the Gurtin–Murdoch and Steigmann–Ogden Surface Energy Endowed Interfaces

Abstract 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.