报告题目： 1. Some remarks on the Gurtin-Murdoch model
报告人：茹重庆 教授 (加拿大阿尔伯塔大学)
It is showed that all equations of the linearized Gurtin-Murdoch model of surface elasticity can be derived, in a straightforward way, from a simple second-order expression for the ratio of deformed surface area to initial surface area. This elementary derivation offers a simple explanation for all unique features of the model and its simplified/modified versions, and helps to clarify some misunderstandings of the model already occurring in the literature. Finally, it is demonstrated that, because the Gurtin-Murdoch model is based on a hybrid formulation combining linearized deformation of bulk material with 2nd-order finite deformation of the surface, caution is needed when the original form of this model is applied to bending deformation of thin-walled elastic structures with surface stress.
报告题目： 2. Non-classical mechanical behavior of elastic membranes of two independent bending rigidities
报告人：茹重庆 教授 (加拿大阿尔伯塔大学)
The present work considers the mechanical behavior of a non-classical elastic membrane with two independent bending rigidities. Our interest focuses on the case when the ratio of the Gaussian bending rigidity to the common flexural rigidity falls within the non-classical range, which cannot be covered by a classical elastic plate with an admissible positive Poisson ratio. Our results for a rectangular elastic membrane with two opposite free edges show that its deflection under a uniform transverse pressure could be considerably (even more than twice) larger than a classical elastic plate under otherwise identical conditions, while its lowest fundamental frequency and critical buckling force could be considerably (even more than 50%) lower than a classical elastic plate under otherwise identical conditions. These unexpected results suggest that, unlike classical elastic plates whose actual mechanical behavior are often insensitive to the value of the admissible positive Poisson ratio, actual mechanical behavior of a non-classical elastic membrane with two independent bending rigidities could be very sensitive to the exact values of the two independent bending rigidities. Therefore, the exact value of the Gaussian bending rigidity could be crucial for such non-classical elastic membranes. Only knowing the values of the flexural rigidity and Poisson ratio is insufficient for accurate prediction of mechanical modeling of such non-classical elastic membranes with two independent bending rigidities (such as some biomembranes and atom-thick monolayer membranes).
Dr. Chongqing Ru is currently a Professor in department of mechanical engineering, University of Alberta, Canada. Dr. Ru received his doctorate in solid mechanics at Peking University (China), and then worked in the Institute of Mechanics, Chinese Academy of Science and held a number of visitor/research positions in several universities in Italy, USA and Canada. He joined the University of Alberta in 1997 and became a Professor in 2004. Dr. Ru’s past research areas include plastic buckling of structures, mechanics of elastic inclusions, electroelastic mechanics, and some applied mathematics problems related to solid mechanics. Besides traditional areas of solid mechanics, his recent research interests include solid mechanics at micro/nano scales, solid mechanics of soft matter, and solid mechanics of thin film materials.