Acta Mechanica Sinica

, Volume 33, Issue 1, pp 173–188 | Cite as

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Research Paper


Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipolar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar tractions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consideration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy partition between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.


Gradient elasticity Interfacial condition Energy flux ratio Amplitude ratio Dipolar traction 



The project was supported by the Fundamental Research Funds for the Central Universities (Grant FRF-BR-15-026A), the State science and technology support program (Grant 2013BAK12B08), the HeiLongJiang Natural Science Fund (Grant B2015019), and the National Natural Science Foundation of China (Grant 10972029).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsQiqihar UniversityQiqiharChina
  2. 2.Department of Applied MechanicsUniversity of Sciences and Technology BeijingBeijingChina

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