**“Two Higher-Order Elasticity Theories and Their Applications
at Micron and Nanometer Scales”**

Dr. Xin-Lin Gao, Texas A&M University

**Abstract**

Lacking a material length scale parameter, classical elasticity cannot interpret microstructure-dependent size effects observed in numerous experiments at micron and nanometer scales. Higher-order elasticity theories contain additional material parameters and are capable of explaining these size effects. Two such theories, including their variational formulations and applications, will be discussed in this seminar based on the recent work of the speaker’s group. One of the two is a simplified strain gradient elasticity theory that contains two Lamé’s constants and one material length scale parameter. As a direct application of the theory, an analytical solution for the pressurized thick-walled cylindrical shell problem has been obtained, which reduces to Lamé’s classical solution when the strain gradient effect is not considered. Also a general solution of the Eshelby-type inclusion problem has been analytically derived using this theory. The resulting fourth-order Eshelby tensor is essential for homogenization analysis and design of composite materials. The other is a modified couple stress elasticity theory, which involves one material length scale parameter. By applying this theory directly, the solution of a simple shear problem has been analytically obtained, which can capture the boundary layer effect revealed by molecular dynamics simulations. Based on this theory and Hamilton’s principle, a microstructure-dependent Timoshenko beam model has also been developed, in which both bending and axial deformations are considered and the Poisson effect is incorporated. This newly developed beam model recovers the classical Timoshenko beam theory when the material length scale parameter and Poisson’s ratio are both set to be zero.

**Biography**

Xin-Lin Gao is an associate professor of mechanical engineering and materials science and engineering at Texas A&M. He is also a chaired professor (visiting) at East China University of Science and Technology in Shanghai. His other experience includes working at AFIT and AFRL at Wright-Patterson Air Force Base for two years. He holds a master’s in engineering mechanics (1997) and a PhD in mechanical engineering with a minor in mathematics (1998), both from the University of Wisconsin-Madison. He has conducted research in a variety of areas in mechanics and materials and is an author/co-author of 73 journal papers and 76 conference publications. His research has been funded by NSF, AFOSR, AFRL, the U.S. Army, DOE and industry, he has been a PI or co-PI on research projects worth over $7.2 million, and he was recently elected an ASME fellow.