Optimal lower bounds on the local stress inside random thermoelastic composites
Yue Chen,Robert Lipton +1 more
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In this paper, a methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading.Abstract:
A methodology is presented for bounding all higher moments of the local hydrostatic stress field inside random two phase linear thermoelastic media undergoing macroscopic thermomechanical loading. The method also provides a lower bound on the maximum local stress. Explicit formulae for the optimal lower bounds are found that are expressed in terms of the applied macroscopic thermal and mechanical loading, coefficients of thermal expansion, elastic properties, and volume fractions. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to the applied loads and the thermal stresses inside each phase. These bounds are shown to be the best possible in that they are attained by the Hashin-Shtrikman coated sphere assemblage.read more
Citations
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Uncertain loading and quantifying maximum energy concentration within composite structures
TL;DR: A systematic method is introduced for identifying the worst case load among all boundary loads of fixed energy and applying this computational method to bound the best case load associated with an ensemble of random boundary loads given by a second order random process.
Journal ArticleDOI
Criteria for guaranteed breakdown in two-phase inhomogeneous bodies
Patrick Bardsley,Michael S. Primrose,Michael Zhao,Jonathan Boyle,Nathan Briggs,Zoe Koch,Graeme W. Milton +6 more
TL;DR: In this article, the maximum field strength in one or both phases in a body containing two-phases is derived for conductivity, with one or two sets of boundary conditions, for complex conductivity and for two-dimensional elasticity.
Journal ArticleDOI
Geometries of inhomogeneities with minimum field concentration
TL;DR: In this paper, a new class of geometries, namely, E-inclusions and periodic Einclusions, are shown to be optimal with minimum field concentration and minimum strain or stress concentration.
Journal ArticleDOI
New bounds on local strain fields inside random heterogeneous materials
Bacim Alali,Robert Lipton +1 more
TL;DR: In this article, a methodology is presented for bounding the higher L p norms, 2 ⩽ p⩽ ∞, of the local strain inside random media, and optimal lower bounds are given in terms of the applied loading and volume fractions for random two phase composites.
Journal ArticleDOI
Criteria for guaranteed breakdown in two-phase inhomogeneous bodies
Patrick Bardsley,Michael S. Primrose,Michael Zhao,Jonathan Boyle,Nathan Briggs,Zoe Koch,Graeme W. Milton +6 more
TL;DR: In this article, lower bounds on the maximum field strength in one or both phases in a body containing two-phases are derived for conductivity, with one or two sets of boundary conditions.
References
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Book
Elliptic Partial Differential Equations of Second Order
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TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
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Elastic properties of reinforced solids: some theoretical principles
TL;DR: In this paper, an elementary account of several theoretical methods of attack is given, among them the derivation of inequalities between various moduli, and the approach is completely general and exact.
Journal ArticleDOI
Colours in Metal Glasses and in Metallic Films
TL;DR: In this paper, it was shown that the presence of many of these minute spheres to a wave-length of light in the glass will account for all the optical properties of "regular" gold ruby glass, and that the irregularities in colour and in polarisation effects sometimes exhibited by gold glass are due to excessive distance between consecutive gold particles or to excessive size of such particles.