Strong convergence of the solutions of the linear elasticity and   uniformity of asymptotic expansions in the presence of small inclusions
  We consider the Lam\'e system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lam\'e system converge in appropriate $H^1$-norms when the shear modulus tends to infinity (the other modulus, the compressional modulus is fixed), and when the bulk modulus and the shear modulus tend to zero. Using this result, we show that the asymptotic expansion of the displacement vector in the presence of small inclusion is uniform with respect to Lam\'e parameters. 
Habib Ammari, Hyeonbae Kang, Kyoungsun Kim, Hyundae Lee
math.AP