TY - JOUR

T1 - Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

AU - Cooper, Shane

PY - 2013/10/10

Y1 - 2013/10/10

N2 - A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.

AB - A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.

UR - http://dx.doi.org/10.1080/00036811.2013.833327

U2 - 10.1080/00036811.2013.833327

DO - 10.1080/00036811.2013.833327

M3 - Article

VL - 93

SP - 1401

EP - 1430

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 7

ER -