Asymptotic analysis of solutions to transmission problems in solids with many inclusions

2016/07/20 by Michael Nieves, Nieves, Michael
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Asphalt Pavement Performance Evaluation #Composite Material Mechanics #Contact Mechanics and Variational Inequalities #cond-mat.mtrl-sci #math.AP

paper · pdf · doi:10.48550/arxiv.1607.06347

30 pages, 5 figures

arxiv created 2016/07/20 · arxiv updated 2016/07/22

Abstract

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the nominal diameter of individual inclusions and their separation within the cluster. These small parameters can be comparable to each other. Remainder estimates of the asymptotic approximation are rigorously justified. Numerical illustrations demonstrate the efficiency of the asymptotic approach when compared with benchmark finite element algorithms.

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