Journal Tittle: Acta Mechanica Sinica
Article Tittle: Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling
Author: Wei-Qiu Chen
Abstract: Significant progress has been made in mixed boundary-value problems associated with three-dimensional (3D) crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials. These include material anisotropy and multifield coupling, two typical characteristics of most current multifunctional materials. In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V. I. Fabrikant, whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory. We are particularly interested in crack and contact problems with certain nonlinear features. Emphasis is also placed on the coupling between the temperature field (or the like) and other physical fields (e.g., elastic, electric, and magnetic fields). We further highlight the practical significance of 3D contact solutions, in particular in applications related to modern scanning probe microscopes.
Keywords: Crack Contact; Mixed boundary-value problem; Transverse isotropy; Multifield coupling; Potential theory; Exact solution; Scanning probe microscope
The author recorded a Chinese doggerel to end the paper:
势论出妙法，老树绽新枝。
多场虽耦合，三维可解析。
若呈非线性，或凭巧与技。
大道煌煌在，吾曹应着力。
(Novel methods emerge in potential theory, like new branches bursting on an old tree. Though multiple fields usually get entangled, related 3D problems may be analytically solvable as we could see. When nonlinearity shows up, skills become necessary in search of the key. The greatest truths are the simplest, and we should make more effort to find them just as a bee.)
Please go to the website to read this article: http://link.springer.com/article/10.1007/s10409-015-0509-3