Figure 11.3: Matrix with Inclusion
The force exerted by the matrix on the inclusion is the material force. When an inclusion is incorporated
into a stress-free elastic body, the entire body undergoes a deformation, resulting in a configurational
change of the body (or matrix) from its original state. The change in the total energy due to the deform-
ation is characterized by the material force. The material force is typically calculated by evaluating the
energy-momentum tensor (or Eshelby [ 17 ] stress tensor).
When the inclusion undergoes a uniform deformation, both the matrix and the inclusion experience
an elastic stress field. Now, consider the following figure:
Figure 11.4: Thought Experiment Proposed by Eshelby
No forces are applied to the inclu-
sion or to the matrix. Because theA. Isolate the inclusion from the matrix:inclusion is now isolated, it under-
goes a homogenous deformation.
The strains experienced by the in-
clusion are called eigenstrains. The
matrix remains stress- and strain-
free.The elastic strains induced in the
inclusion due to applied surfaceRecover the original shape of inclusion by applying surface
forces on the inclusion:B.traction cancel out the eigen-Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationFracture Mechanics