The Pole-Zero Constitutive Material Law
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
Model Structure
Myocardial tissue consists of layers of interconnected sheets of tissue, separated by cleavage planes. The muscle fibres lie in the plane of a sheet, and adjacent fibres are coupled more strongly in the plane of the sheet than traverse to it. This results in three microstructural axes:
one along the fibre direction called the fibre axis;
one orthogonal to the fibre axis but also in the plane of the sheet called the sheet axis; and
one which is orthogonal to these two, directed across the cleavage planes called the sheet normal.
The most obvious difference in the material behaviour of the myocardial tisue along these three axes is the limiting strain for an elastic response. Another feature of the biaxial tests is that the stress-strain curve along one axis is almost independent of the degree of lateral stretch. To account for these microstructural properties, a strain energy function called the pole-zero law has been proposed (see below). By using a separate pole for each microstructurally defined axis, the different strain limiting behaviour along each axis is accounted for without the need for numerically unstable, large exponents which are needed in exponential or power law expressions.
The original paper reference is cited below:
Computational mechanics of the heart: from tissue structure to
ventricular function,
M P Nash and P J Hunter,
Journal of Elasticity 61(1/3): 113-141, 2000.
P
Hunter
J
The University of Auckland
The Bioengineering Institute
A pole-zero constitutive law for myocardium
382
303
318
2004-08-10
e.remme@auckland.ac.nz
1995
keyword
myocardium
pole-zero
mechanical constitutive laws
A pole-zero constitutive law for myocardium
382
303
318
1995-00-00 00:00
Added metadata to the model.
P
Hunter
J
Journal of Biomechanical Engineering
B
Smaill
H
Journal of Biomechanical Engineering
I
Hunter
W
I
Hunter
W
Espen
Remme
Catherine
Lloyd
M
2004-05-03T00:00:00+00:00
This is a CellML version of the pole-zero law. CellML is being used to define passive material laws for use in solving finite elasticity problems.
B
Smaill
H