Chemistry Reference
In-Depth Information
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9.2.2.1.3
MORI- TANAKA MODEL
The Mori-Tanaka model is uses for prediction an elastic stress field for in
and around an ellipsoidal reinforcement in an infinite matrix. This method
is based on Eshebly's model. Longitudinal and transverse elastic modulus,
E
11
and E
22
, for isotropic matrix and directed spherical reinforcement are:
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where is the modulus of the matrix, is the volume fraction of reinforce-
ment, is the Poisson's ratio of the matrix, parameters, A
0
, A
1
, …, A
5
are
functions of the Eshelby's tensor.
9.2.2.2
FINITE ELEMENT METHODS
The traditional framework in mechanics has always been the continuum.
Under this framework, materials are assumed to be composed of a divis-
ible continuous medium, with a constitutive relation that remains the same
for a wide range of system sizes. Continuum equations are typically in the
form of deterministic or stochastic partial differential equation (FDE's).
The underling atomic structure of matter is neglected altogether and is re-
placed with a continuous and differentiable mass density. Similar replace-
ment is made for other physical quantities such as energy and momentum.
Differential equations are then formulated from basic physical principles,
such as the conservation of energy or momentum. There are a large variety
