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We can define then an average medium, which has the same integral
properties as the original heterogeneous medium:
 

 
 (16) 
For the homogeneous equivalent we know that it is energetically
equivalent but in the interior stress distribution different
from the heterogeneous medium. They share the same integral properties,
and the stress and strain will be on the average equivalent.
Taking the heterogeneous medium and applying a static force to its exterior
boundaries results in a static stress and strain distribution within the
body. This means stress and strain are functions of the spatial coordinates
only. The stress and strain values are uniquely determined by
the stiffness and by the external forces applied to the exterior surface.
If we apply the same external forces to the homogeneous medium we will
in general not end up with the same displacements as observed in the
heterogeneous case, but on the average over a region much larger than
the scale of the heterogeneity we will have the same result.
Next: Conclusions
Up: Karrenbach: Equivalent Medium
Previous: Energy at a discontinuity
Stanford Exploration Project
1/13/1998