Internal resonances and relaxation memory kernels in composites.

Clicks: 217
ID: 67282
2020
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Ranked #35 of 69 articles by views in philosophical transactions series a, mathematical, physical, and engineering sciences

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Abstract
In heterogeneous composite materials, the behaviour of the medium on larger scales is determined by the microgeometry and properties of the constituents on finer scales. To model the influence of the microlevel processes in composite materials, they are described as materials with memory in which the constitutive relations between stress and strain are given as time-domain convolutions with some relaxation kernel. The paper reveals the relationship between the viscoelastic relaxation kernel and the spectral measure in the Stieltjes integral representation of the effective properties of composites. This spectral measure contains all information about the microgeometry of the material, thus providing a link between the relaxation kernel and the microstructure of the composite. We show that the internal resonances of the microstructure determine the characteristic relaxation times of the fading memory kernel and can be used to introduce a set of internal variables that captures dissipation at the microscale. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.
Reference Key
cherkaev2020internalphilosophical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Cherkaev, Elena;
Journal philosophical transactions series a, mathematical, physical, and engineering sciences
Year 2020
DOI
10.1098/rsta.2019.0106
URL
Keywords
stieltjes analytic representation internal variables relaxation function

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