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.
基金
Financial support of the Natural Science and Engineering Research Council (NSERC)
