On the problem of a thin rigid inclusion embedded in a Maxwell material

  • T. Popova
  • G. A. RogersonEmail author


We consider a plane viscoelastic body, composed of Maxwell material, with a crack and a thin rigid inclusion. The statement of the problem includes boundary conditions in the form of inequalities, together with an integral condition describing the equilibrium conditions of the inclusion. An equivalent variational statement is provided and used to prove the uniqueness of the problem’s solution. The analysis is carried out in respect of perfect and non-perfect bonding of the rigid inclusion. Additional smoothness properties of the solutions, namely the existence of the time derivative, are also established.

Mathematics Subject Classification

74D99 74G25 74G30 


Viscoelasticity Crack Rigid inclusion Variational inequality Inequality-type boundary conditions Non-penetration condition 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsNorth-Eastern Federal UniversityYakutskRussia
  2. 2.School of Computing and MathematicsKeele UniversityKeeleUK

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