(untitled) (Archives of Mechanics - Test, 1998)
In this note we are concerned with (linearized) elastic media that are heterogeneous on the microscale and homogeneous on the macroscale. We assume the validity of an ergodic hypothesis so that we can form ensemble averages such as mean stress âŸ¨σâŸ© and mean strain âŸ¨εâŸ©. We argue that âŸ¨σâŸ© = 0 does not, in general, imply that also âŸ¨εâŸ© = 0 (end of Sec. 2). This is the case, for instance, when the distribution of the stress sources (external forces or incompatibilities) are correlated with the spatial distribution of the local elastic moduli. It is shown how problems of this type can be treated.