Strong convergence of the solutions of the linear elasticity and uniformity of asymptotic expansions in the presence of small inclusions

2012/12/31 by Habib Ammari, Hyeonbae Kang, Ammari, Habib +5
Computer Science · Engineering · Mathematics · #35J47 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Composite Material Mechanics #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35J47

paper · pdf · doi:10.48550/arxiv.1212.6889

20 pages

arxiv created 2012/12/31 · openalex publication_date 2012/12/31 · arxiv updated 2013/01/01 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We consider the Lamé system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lamé system converge in appropriate H¹-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 Lamé parameters.

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