Field fluctuations in a heterogeneous elastic material - An information theory approach. (English) Zbl 0598.73004
The subject is related to randomly disordered solids as polycrystals or multiphase materials. The tensor of elastic constants is a random function of position. A joint probability density functional of elastic constants and displacements is introduced and its entropy is defined by a double functional integral. The functional which maximizes the entropy and agrees with constraints is derived. An approximate solution is given for a case when one-point probability density is available only. Effective elastic properties are connected with the topological order and fluctuations of the strain field. A composite material which consists of N isotropic components is taken as an example. The Gauss probability distributions are obtained for the stress and strain and mean values and fluctuations of stresses are calculated for a cemented metal carbide and a zinc polycrystal. A solution of the variational problem where the random field is subject to constraints, is presented in an appendix.
Reviewer: J.Murzewski
MSC:
| 74A40 | Random materials and composite materials |
| 74E05 | Inhomogeneity in solid mechanics |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 74E15 | Crystalline structure |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74A60 | Micromechanical theories |
| 74M25 | Micromechanics of solids |
| 62B10 | Statistical aspects of information-theoretic topics |
Keywords:
internal stress; strain fields; information theory entropy is maximized subject to constraints; equations of elasticity; experimental data; polycrystals; multiphase materials; Gauss probability distributionsReferences:
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