Abstract
The concept of the modified Green function, defined as certain second derivatives of the conventional tensor Green function, has been proved useful in solving elastic (and other) problems in the media of complicated constitution, such as heterogeneous or anisotropic continua. Emphasis is laid on infinite media. Contrary to the conventional approach, situations with finite stress and strain in the infinite regions are also investigated. Depending on the conditions four modified Green functions appear. These are limits of the four (modified) Green functions of finite bodies that grow beyond bounds. Certain properties of these functions are illustrated of the two basic boundary value problems of potential theory, assuming that the growing bodies are spheres. It is shown that the concept of modified Green functions is particularly useful in the elasticity theory of random media.
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Kröner, E. (1990). Modified Green Functions in the Theory of Heterogeneous and/or Anisotropic Linearly Elastic Media. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_13
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DOI: https://doi.org/10.1007/978-1-4613-8919-4_13
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