Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions  

作　　者：Ru C. Q. Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2010年第3期536-544,共9页中国科学：物理学、力学、天文学（英文版）

基　　金：Financial support of the Natural Science and Engineering Research Council (NSERC)

摘　　要：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.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.

关 键 词：SURFACE ELASTICITY SURFACE stress Gurtin-Murdoch model 

分 类 号：O347.4[理学—固体力学]