- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2015-11-09 15:52:21+13:00
- Desc:
- consolidate on new version of Guccione model tidied up by Vicky Wang
- Permanent Source URI:
- https://models.cellml.org/workspace/guccione_mcculloch_waldman_1991/rawfile/0fbaeafd68b25502517218bfd259aac657a9b527/guccione_mcculloch_waldman_1991.cellml
<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="PoleZero" name="guccione_mcculloch_waldman_1991_version03">
<!-- Global units -->
<units name="strain">
<unit units="dimensionless"/>
</units>
<units name="stress">
<unit units="dimensionless"/>
</units>
<component name="interface" cmeta:id="interface">
<!-- Variables we expect to be set/controlled externally -->
<variable units="strain" private_interface="out" name="E11"/>
<variable units="strain" private_interface="out" name="E22"/>
<variable units="strain" private_interface="out" name="E33"/>
<variable units="strain" private_interface="out" name="E12"/>
<variable units="strain" private_interface="out" name="E13"/>
<variable units="strain" private_interface="out" name="E23"/>
<variable units="strain" private_interface="out" name="aff" initial_value="0"/>
<variable units="strain" private_interface="out" name="afn" initial_value="0"/>
<variable units="strain" private_interface="out" name="afs" initial_value="0"/>
<variable units="strain" private_interface="out" name="ann" initial_value="0"/>
<variable units="strain" private_interface="out" name="ans" initial_value="0"/>
<variable units="strain" private_interface="out" name="ass" initial_value="0"/>
<variable units="strain" private_interface="out" name="bff" initial_value="0"/>
<variable units="strain" private_interface="out" name="bfn" initial_value="0"/>
<variable units="strain" private_interface="out" name="bfs" initial_value="0"/>
<variable units="strain" private_interface="out" name="bnn" initial_value="0"/>
<variable units="strain" private_interface="out" name="bns" initial_value="0"/>
<variable units="strain" private_interface="out" name="bss" initial_value="0"/>
<variable units="strain" private_interface="out" name="kff" initial_value="0"/>
<variable units="strain" private_interface="out" name="kfn" initial_value="0"/>
<variable units="strain" private_interface="out" name="kfs" initial_value="0"/>
<variable units="strain" private_interface="out" name="knn" initial_value="0"/>
<variable units="strain" private_interface="out" name="kns" initial_value="0"/>
<variable units="strain" private_interface="out" name="kss" initial_value="0"/>
<!-- Variables we want to make available externally -->
<variable units="stress" public_interface="out" private_interface="in" name="Tdev11"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev22"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev33"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev12"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev13"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev23"/>
</component> <!--interface-->
<component name="equations" cmeta:id="equations">
<!-- Inputs -->
<variable units="strain" public_interface="in" name="E11"/>
<variable units="strain" public_interface="in" name="E22"/>
<variable units="strain" public_interface="in" name="E33"/>
<variable units="strain" public_interface="in" name="E12"/>
<variable units="strain" public_interface="in" name="E13"/>
<variable units="strain" public_interface="in" name="E23"/>
<variable units="strain" public_interface="in" name="aff"/>
<variable units="strain" public_interface="in" name="afn"/>
<variable units="strain" public_interface="in" name="afs"/>
<variable units="strain" public_interface="in" name="ann"/>
<variable units="strain" public_interface="in" name="ans"/>
<variable units="strain" public_interface="in" name="ass"/>
<variable units="strain" public_interface="in" name="bff"/>
<variable units="strain" public_interface="in" name="bfn"/>
<variable units="strain" public_interface="in" name="bfs"/>
<variable units="strain" public_interface="in" name="bnn"/>
<variable units="strain" public_interface="in" name="bns"/>
<variable units="strain" public_interface="in" name="bss"/>
<variable units="strain" public_interface="in" name="kff"/>
<variable units="strain" public_interface="in" name="kfn"/>
<variable units="strain" public_interface="in" name="kfs"/>
<variable units="strain" public_interface="in" name="knn"/>
<variable units="strain" public_interface="in" name="kns"/>
<variable units="strain" public_interface="in" name="kss"/>
<!-- Outputs computed here -->
<variable units="stress" public_interface="out" name="Tdev11"/>
<variable units="stress" public_interface="out" name="Tdev22"/>
<variable units="stress" public_interface="out" name="Tdev33"/>
<variable units="stress" public_interface="out" name="Tdev12"/>
<variable units="stress" public_interface="out" name="Tdev13"/>
<variable units="stress" public_interface="out" name="Tdev23"/>
<!-- Temporary variables -->
<variable units="strain" name="elim11"/>
<variable units="strain" name="elim22"/>
<variable units="strain" name="elim33"/>
<variable units="strain" name="elim12"/>
<variable units="strain" name="elim13"/>
<variable units="strain" name="elim23"/>
<variable units="strain" name="etol11"/>
<variable units="strain" name="etol22"/>
<variable units="strain" name="etol33"/>
<variable units="strain" name="etol12"/>
<variable units="strain" name="etol13"/>
<variable units="strain" name="etol23"/>
<variable units="dimensionless" name="tol" initial_value="0.9"/>
<variable units="dimensionless" name="signE11"/>
<variable units="dimensionless" name="signE22"/>
<variable units="dimensionless" name="signE33"/>
<variable units="dimensionless" name="signE12"/>
<variable units="dimensionless" name="signE13"/>
<variable units="dimensionless" name="signE23"/>
<variable units="strain" name="eabs11"/>
<variable units="strain" name="eabs22"/>
<variable units="strain" name="eabs33"/>
<variable units="strain" name="eabs12"/>
<variable units="strain" name="eabs13"/>
<variable units="strain" name="eabs23"/>
<variable units="strain" name="aMeabs11"/>
<variable units="strain" name="aMeabs22"/>
<variable units="strain" name="aMeabs33"/>
<variable units="strain" name="aMeabs12"/>
<variable units="strain" name="aMeabs13"/>
<variable units="strain" name="aMeabs23"/>
<variable units="strain" name="mbffM1"/>
<variable units="strain" name="mbfnM1"/>
<variable units="strain" name="mbfsM1"/>
<variable units="strain" name="mbnnM1"/>
<variable units="strain" name="mbnsM1"/>
<variable units="strain" name="mbssM1"/>
<variable units="strain" name="p11"/>
<variable units="strain" name="p12"/>
<variable units="strain" name="p13"/>
<variable units="strain" name="p22"/>
<variable units="strain" name="p23"/>
<variable units="strain" name="p33"/>
<variable units="strain" name="q11"/>
<variable units="strain" name="q12"/>
<variable units="strain" name="q13"/>
<variable units="strain" name="q22"/>
<variable units="strain" name="q23"/>
<variable units="strain" name="q33"/>
<!-- Calculating strain limits for where the slope-extrapolation starts-->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim11_calculation_eq">
<apply id="elim11_calculation">
<eq/>
<ci>elim11</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>aff</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim22_calculation_eq">
<apply id="elim22_calculation">
<eq/>
<ci>elim22</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>ass</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim33_calculation_eq">
<apply id="elim33_calculation">
<eq/>
<ci>elim33</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>ann</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim12_calculation_eq">
<apply id="elim12_calculation">
<eq/>
<ci>elim12</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>afs</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim13_calculation_eq">
<apply id="elim13_calculation">
<eq/>
<ci>elim13</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>afn</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="elim23_calculation_eq">
<apply id="elim23_calculation">
<eq/>
<ci>elim23</ci>
<apply>
<times/>
<ci>tol</ci>
<ci>ans</ci>
</apply>
</apply>
</math>
<!-- Calculating strain limits for where the slope-extrapolation starts-->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol11_calculation_eq">
<apply id="etol11_calculation">
<eq/>
<ci>etol11</ci>
<apply>
<minus/>
<ci>aff</ci>
<ci>elim11</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol22_calculation_eq">
<apply id="etol22_calculation">
<eq/>
<ci>etol22</ci>
<apply>
<minus/>
<ci>ass</ci>
<ci>elim22</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol33_calculation_eq">
<apply id="etol33_calculation">
<eq/>
<ci>etol33</ci>
<apply>
<minus/>
<ci>ann</ci>
<ci>elim33</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol12_calculation_eq">
<apply id="etol12_calculation">
<eq/>
<ci>etol12</ci>
<apply>
<minus/>
<ci>afs</ci>
<ci>elim12</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol13_calculation_eq">
<apply id="etol13_calculation">
<eq/>
<ci>etol13</ci>
<apply>
<minus/>
<ci>afn</ci>
<ci>elim13</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="etol23_calculation_eq">
<apply id="etol23_calculation">
<eq/>
<ci>etol23</ci>
<apply>
<minus/>
<ci>ans</ci>
<ci>elim23</ci>
</apply>
</apply>
</math>
<!-- Calculation of Signs -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE11_calculation_eq">
<apply id="signE11_calculation">
<eq/>
<ci>signE11</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E11</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE22_calculation_eq">
<apply id="signE22_calculation">
<eq/>
<ci>signE22</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E22</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE33_calculation_eq">
<apply id="signE33_calculation">
<eq/>
<ci>signE33</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E33</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE12_calculation_eq">
<apply id="signE12_calculation">
<eq/>
<ci>signE12</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E12</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE13_calculation_eq">
<apply id="signE13_calculation">
<eq/>
<ci>signE13</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E13</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="signE23_calculation_eq">
<apply id="signE23_calculation">
<eq/>
<ci>signE23</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<geq/>
<ci>E23</ci>
<cn cellml:units="strain">0.0</cn>
</apply>
</piece>
<otherwise>
<cn cellml:units="dimensionless">-1.0</cn>
</otherwise>
</piecewise>
</apply>
</math>
<!-- Calculation of altered constants -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbffM1_calculation_eq">
<apply id="mbffM1_calculation">
<eq/>
<ci>mbffM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bff</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbfnM1_calculation_eq">
<apply id="mbfnM1_calculation">
<eq/>
<ci>mbfnM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bfn</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbfsM1_calculation_eq">
<apply id="mbfsM1_calculation">
<eq/>
<ci>mbfsM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bfs</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbnnM1_calculation_eq">
<apply id="mbnnM1_calculation">
<eq/>
<ci>mbnnM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bnn</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbnsM1_calculation_eq">
<apply id="mbnsM1_calculation">
<eq/>
<ci>mbnsM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bns</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="mbssM1_calculation_eq">
<apply id="mbssM1_calculation">
<eq/>
<ci>mbssM1</ci>
<apply>
<minus/>
<cn cellml:units="strain">-1</cn>
<ci>bss</ci>
</apply>
</apply>
</math>
<!-- Calculation of Absolute values -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs11_calculation_eq">
<apply id="eabs11_calculation">
<eq/>
<ci>eabs11</ci>
<apply>
<times/>
<ci>signE11</ci>
<ci>E11</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs22_calculation_eq">
<apply id="eabs22_calculation">
<eq/>
<ci>eabs22</ci>
<apply>
<times/>
<ci>signE22</ci>
<ci>E22</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs33_calculation_eq">
<apply id="eabs33_calculation">
<eq/>
<ci>eabs33</ci>
<apply>
<times/>
<ci>signE33</ci>
<ci>E33</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs12_calculation_eq">
<apply id="eabs12_calculation">
<eq/>
<ci>eabs12</ci>
<apply>
<times/>
<ci>signE12</ci>
<ci>E12</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs13_calculation_eq">
<apply id="eabs13_calculation">
<eq/>
<ci>eabs13</ci>
<apply>
<times/>
<ci>signE13</ci>
<ci>E13</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="eabs23_calculation_eq">
<apply id="eabs23_calculation">
<eq/>
<ci>eabs23</ci>
<apply>
<times/>
<ci>signE23</ci>
<ci>E23</ci>
</apply>
</apply>
</math>
<!-- Calculation of aMAbs values -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs11_calculation_eq">
<apply id="aMeabs11_calculation">
<eq/>
<ci>aMeabs11</ci>
<apply>
<minus/>
<ci>aff</ci>
<ci>eabs11</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs12_calculation_eq">
<apply id="aMeabs12_calculation">
<eq/>
<ci>aMeabs12</ci>
<apply>
<minus/>
<ci>afs</ci>
<ci>eabs12</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs13_calculation_eq">
<apply id="aMeabs13_calculation">
<eq/>
<ci>aMeabs13</ci>
<apply>
<minus/>
<ci>afn</ci>
<ci>eabs13</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs22_calculation_eq">
<apply id="aMeabs22_calculation">
<eq/>
<ci>aMeabs22</ci>
<apply>
<minus/>
<ci>ass</ci>
<ci>eabs22</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs23_calculation_eq">
<apply id="aMeabs23_calculation">
<eq/>
<ci>aMeabs23</ci>
<apply>
<minus/>
<ci>ans</ci>
<ci>eabs23</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="aMeabs33_calculation_eq">
<apply id="aMeabs33_calculation">
<eq/>
<ci>aMeabs33</ci>
<apply>
<minus/>
<ci>ann</ci>
<ci>eabs33</ci>
</apply>
</apply>
</math>
<!-- Calculation of p&q values values -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p11_calculation_eq">
<apply id="p11_calculation">
<eq/>
<ci>p11</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol11</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bff</ci>
</apply>
</apply>
<ci>kff</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bff</ci>
<ci>elim11</ci>
<ci>signE11</ci>
<apply>
<power/>
<ci>etol11</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bff</ci>
<apply>
<power/>
<ci>elim11</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbffM1</ci>
<apply>
<power/>
<ci>etol11</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q11_calculation_eq">
<apply id="q11_calculation">
<eq/>
<ci>q11</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol11</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bff</ci>
</apply>
</apply>
<ci>kff</ci>
<ci>elim11</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim11</ci>
<ci>bff</ci>
<ci>signE11</ci>
<apply>
<power/>
<ci>etol11</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p11</ci>
<ci>elim11</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p12_calculation_eq">
<apply id="p12_calculation">
<eq/>
<ci>p12</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfs</ci>
</apply>
</apply>
<ci>kfs</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bfs</ci>
<ci>elim12</ci>
<ci>signE12</ci>
<apply>
<power/>
<ci>etol12</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfs</ci>
<apply>
<power/>
<ci>elim12</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbfsM1</ci>
<apply>
<power/>
<ci>etol12</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q12_calculation_eq">
<apply id="q12_calculation">
<eq/>
<ci>q12</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfs</ci>
</apply>
</apply>
<ci>kfs</ci>
<ci>elim12</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim12</ci>
<ci>bfs</ci>
<ci>signE12</ci>
<apply>
<power/>
<ci>etol12</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p12</ci>
<ci>elim12</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p13_calculation_eq">
<apply id="p13_calculation">
<eq/>
<ci>p13</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol13</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfn</ci>
</apply>
</apply>
<ci>kfn</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bfn</ci>
<ci>elim13</ci>
<ci>signE13</ci>
<apply>
<power/>
<ci>etol13</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfn</ci>
<apply>
<power/>
<ci>elim13</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbfnM1</ci>
<apply>
<power/>
<ci>etol13</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q13_calculation_eq">
<apply id="q13_calculation">
<eq/>
<ci>q13</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol13</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfn</ci>
</apply>
</apply>
<ci>kfn</ci>
<ci>elim13</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim13</ci>
<ci>bfn</ci>
<ci>signE13</ci>
<apply>
<power/>
<ci>etol13</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p13</ci>
<ci>elim13</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p22_calculation_eq">
<apply id="p22_calculation">
<eq/>
<ci>p22</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bss</ci>
</apply>
</apply>
<ci>kss</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bss</ci>
<ci>elim22</ci>
<ci>signE22</ci>
<apply>
<power/>
<ci>etol22</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bss</ci>
<apply>
<power/>
<ci>elim22</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbssM1</ci>
<apply>
<power/>
<ci>etol22</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q22_calculation_eq">
<apply id="q22_calculation">
<eq/>
<ci>q22</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bss</ci>
</apply>
</apply>
<ci>kss</ci>
<ci>elim22</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim22</ci>
<ci>bss</ci>
<ci>signE22</ci>
<apply>
<power/>
<ci>etol22</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p22</ci>
<ci>elim22</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p23_calculation_eq">
<apply id="p23_calculation">
<eq/>
<ci>p23</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bns</ci>
</apply>
</apply>
<ci>kns</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bns</ci>
<ci>elim23</ci>
<ci>signE23</ci>
<apply>
<power/>
<ci>etol23</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bns</ci>
<apply>
<power/>
<ci>elim23</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbnsM1</ci>
<apply>
<power/>
<ci>etol23</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q23_calculation_eq">
<apply id="q23_calculation">
<eq/>
<ci>q23</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bns</ci>
</apply>
</apply>
<ci>kns</ci>
<ci>elim23</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim23</ci>
<ci>bns</ci>
<ci>signE23</ci>
<apply>
<power/>
<ci>etol23</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p23</ci>
<ci>elim23</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="p33_calculation_eq">
<apply id="p33_calculation">
<eq/>
<ci>p33</ci>
<apply>
<times/>
<apply>
<power/>
<ci>etol33</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bnn</ci>
</apply>
</apply>
<ci>knn</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>bnn</ci>
<ci>elim33</ci>
<ci>signE33</ci>
<apply>
<power/>
<ci>etol33</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bnn</ci>
<apply>
<power/>
<ci>elim33</ci>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
<ci>mbnnM1</ci>
<apply>
<power/>
<ci>etol33</ci>
<cn cellml:units="dimensionless">-2.0</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q33_calculation_eq">
<apply id="q33_calculation">
<eq/>
<ci>q33</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<power/>
<ci>etol33</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bnn</ci>
</apply>
</apply>
<ci>knn</ci>
<ci>elim33</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>elim33</ci>
<ci>bnn</ci>
<ci>signE33</ci>
<apply>
<power/>
<ci>etol33</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>p33</ci>
<ci>elim33</ci>
</apply>
</apply>
</apply>
</math>
<!-- Calculation of Stress -->
<!-- 11 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev11_calculation_eq">
<apply id="Tdev11_calculation">
<eq/>
<ci>Tdev11</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs11</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bff</ci>
</apply>
</apply>
<ci>kff</ci>
<ci>E11</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E11</ci>
<ci>bff</ci>
<ci>signE11</ci>
<apply>
<power/>
<ci>aMeabs11</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs11</ci>
<ci>elim11</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p11</ci>
<ci>E11</ci>
</apply>
<ci>q11</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- 22 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev22_calculation_eq">
<apply id="Tdev22_calculation">
<eq/>
<ci>Tdev22</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs22</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bss</ci>
</apply>
</apply>
<ci>kss</ci>
<ci>E22</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E22</ci>
<ci>bss</ci>
<ci>signE22</ci>
<apply>
<power/>
<ci>aMeabs22</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs22</ci>
<ci>elim22</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p22</ci>
<ci>E22</ci>
</apply>
<ci>q22</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- 33 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev33_calculation_eq">
<apply id="Tdev33_calculation">
<eq/>
<ci>Tdev33</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs33</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bnn</ci>
</apply>
</apply>
<ci>knn</ci>
<ci>E33</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E33</ci>
<ci>bnn</ci>
<ci>signE33</ci>
<apply>
<power/>
<ci>aMeabs33</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs33</ci>
<ci>elim33</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p33</ci>
<ci>E33</ci>
</apply>
<ci>q33</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- 12 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev12_calculation_eq">
<apply id="Tdev12_calculation">
<eq/>
<ci>Tdev12</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs12</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfs</ci>
</apply>
</apply>
<ci>kfs</ci>
<ci>E12</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E12</ci>
<ci>bfs</ci>
<ci>signE12</ci>
<apply>
<power/>
<ci>aMeabs12</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs12</ci>
<ci>elim12</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p12</ci>
<ci>E12</ci>
</apply>
<ci>q12</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- 13 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev13_calculation_eq">
<apply id="Tdev13_calculation">
<eq/>
<ci>Tdev13</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs13</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bfn</ci>
</apply>
</apply>
<ci>kfn</ci>
<ci>E13</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E13</ci>
<ci>bfn</ci>
<ci>signE13</ci>
<apply>
<power/>
<ci>aMeabs13</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs13</ci>
<ci>elim13</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p13</ci>
<ci>E13</ci>
</apply>
<ci>q13</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- 23 direction -->
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev23_calculation_eq">
<apply id="Tdev23_calculation">
<eq/>
<ci>Tdev23</ci>
<piecewise>
<piece>
<apply>
<times/>
<apply>
<power/>
<ci>aMeabs23</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">-1.0</cn>
<ci>bns</ci>
</apply>
</apply>
<ci>kns</ci>
<ci>E23</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.0</cn>
<apply>
<times/>
<ci>E23</ci>
<ci>bns</ci>
<ci>signE23</ci>
<apply>
<power/>
<ci>aMeabs23</ci>
<cn cellml:units="dimensionless">-1.0</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<leq/>
<ci>eabs23</ci>
<ci>elim23</ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci>p23</ci>
<ci>E23</ci>
</apply>
<ci>q23</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<!-- END END END END END END END END END END END END END END END -->
</component>
<!--membrane-->
<connection>
<map_components component_2="equations" component_1="interface"/>
<map_variables variable_2="E11" variable_1="E11"/>
<map_variables variable_2="E22" variable_1="E22"/>
<map_variables variable_2="E33" variable_1="E33"/>
<map_variables variable_2="E12" variable_1="E12"/>
<map_variables variable_2="E13" variable_1="E13"/>
<map_variables variable_2="E23" variable_1="E23"/>
<map_variables variable_2="Tdev11" variable_1="Tdev11"/>
<map_variables variable_2="Tdev22" variable_1="Tdev22"/>
<map_variables variable_2="Tdev33" variable_1="Tdev33"/>
<map_variables variable_2="Tdev12" variable_1="Tdev12"/>
<map_variables variable_2="Tdev13" variable_1="Tdev13"/>
<map_variables variable_2="Tdev23" variable_1="Tdev23"/>
<map_variables variable_2="aff" variable_1="aff"/>
<map_variables variable_2="afn" variable_1="afn"/>
<map_variables variable_2="afs" variable_1="afs"/>
<map_variables variable_2="ann" variable_1="ann"/>
<map_variables variable_2="ans" variable_1="ans"/>
<map_variables variable_2="ass" variable_1="ass"/>
<map_variables variable_2="bff" variable_1="bff"/>
<map_variables variable_2="bfn" variable_1="bfn"/>
<map_variables variable_2="bfs" variable_1="bfs"/>
<map_variables variable_2="bnn" variable_1="bnn"/>
<map_variables variable_2="bns" variable_1="bns"/>
<map_variables variable_2="bss" variable_1="bss"/>
<map_variables variable_2="kff" variable_1="kff"/>
<map_variables variable_2="kfn" variable_1="kfn"/>
<map_variables variable_2="kfs" variable_1="kfs"/>
<map_variables variable_2="knn" variable_1="knn"/>
<map_variables variable_2="kns" variable_1="kns"/>
<map_variables variable_2="kss" variable_1="kss"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="equations"/>
</component_ref>
</group>
</model>
