Field fluctuations in a heterogeneous elastic material - An information theory approach
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.
information theory entropy is maximized subject to constraints
scientific article; zbMATH DE number 3965517