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Solution of statistical problems in elasticity theory in the singular approximation

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Abstract

A method of calculating elastic fields and effective moduli of microheterogeneous solids is developed in the random field theory. The solution is obtained in the form of an operator series, each term of which is constructed on the basis of the regular component of the second derivative tensor of the equilibrium Green function. The zeroth approximation of such a series consists of the local part of the interaction between inhomogeneity grains. The possibilities of the method are illustrated on the example of an isotropic mixture of two isotropic components.

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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 98–102, January–February, 1972.

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Fokin, A.G. Solution of statistical problems in elasticity theory in the singular approximation. J Appl Mech Tech Phys 13, 85–89 (1972). https://doi.org/10.1007/BF00852360

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Keywords

  • Mechanical Engineer
  • Field Theory
  • Industrial Mathematic
  • Green Function
  • Statistical Problem