From 257329bc4680c896f678201dd8041a1a9116f0b4 Mon Sep 17 00:00:00 2001 From: German Date: Mon, 9 Jan 2023 10:58:46 +0000 Subject: [PATCH 1/4] Adding tech demo 15 --- .../graphics/gtec_calvalhyper_fig1.gif | Bin 0 -> 24819 bytes .../graphics/gtec_calvalhyper_fig10.gif | Bin 0 -> 22939 bytes .../graphics/gtec_calvalhyper_fig2.gif | Bin 0 -> 24340 bytes .../graphics/gtec_calvalhyper_fig3.gif | Bin 0 -> 13985 bytes .../graphics/gtec_calvalhyper_fig4.gif | Bin 0 -> 13045 bytes .../graphics/gtec_calvalhyper_fig5.gif | Bin 0 -> 35608 bytes .../graphics/gtec_calvalhyper_fig6.gif | Bin 0 -> 59691 bytes .../graphics/gtec_calvalhyper_fig7.gif | Bin 0 -> 52067 bytes .../graphics/gtec_calvalhyper_fig8.gif | Bin 0 -> 54565 bytes .../graphics/gtec_calvalhyper_fig9.gif | Bin 0 -> 28309 bytes .../techdemo-15/p_ex_15-teccalvalhyper.rst | 442 ++++++++++++++++++ 11 files changed, 442 insertions(+) create mode 100755 doc/source/technology_showcase_examples/techdemo-15/graphics/gtec_calvalhyper_fig1.gif 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+---------------------------------------------------------------------------------------------- + +This example problem demonstrates the hyperelastic curve-fitting capabilities used to select constitutive model +parameters to fit experimental data. Several issues that influence the accuracy of the curve fit are discussed. +Validation of the resulting constitutive model is demonstrated by comparison with a +tension-torsion experiment. + +The following topics are available: + +* `15.1. Introduction`_ +* `15.2. Problem Description`_ +* `15.3. Material Properties`_ +* `15.4. Analysis and Solution Controls`_ +* `15.5. Results and Discussion`_ +* `15.6. Recommendations`_ +* `15.7. References`_ +* `15.8. Input Files`_ + +You can also perform this example analysis entirely in the Ansys +Mechanical Application. For more information, see +*Calibrating and Validating a Hyperelastic Constitutive Model in the Workbench Technology Showcase: Example Problems*. + +15.1. Introduction +------------------ + +Several hyperelastic constitutive models can be used to model the large deformation +behavior of elastic materials; however, it is sometimes difficult to select parameters +to adequately match the behavior of the material. The curve-fitting process fits the hyperelastic +constitutive model parameters to a set of experimental data using a least-squares +minimization. + +Curve-fitting is relatively simple, but certain conditions can affect the accuracy of +the resulting constitutive model. The constitutive model should therefore be compared +with experimental data to ensure that it adequately reproduces the material behavior +over the actual range of deformation. + +15.2. Problem Description +------------------------- + +A constitutive model is needed that matches the behavior of a vulcanized natural +rubber material up to 100 percent engineering strain in a variety of deformation modes. + +In this problem, the experimental data are obtained from a simulation of a +hyperelastic test suite (uniaxial, biaxial, and planar tension tests) using common +experimental test specimens. Using this data, parameters for a constitutive model are +determined using hyperelastic fitting capabilities that focus on use of the three-, +five-, and nine-parameter Mooney-Rivlin hyperelastic models. + +After demonstrating the fitting procedure and selecting a suitable constitutive model, +a tension-torsion experiment is simulated and compared to the experimental data to +validate the predictions for the model. + +15.3. Material Properties +------------------------- + +Material properties for the calibration and validation experiments follow: + +* `15.3.1. Calibration Experiments`_ +* `15.3.2. Validation Experiment`_ + +15.3.1. Calibration Experiments +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Experimental data was obtained via a simulation of a hyperelastic test suite with +an Ogden hyperelastic material. The test suite specimens are shown here, with the +dark areas indicating locations of the clamps: + +.. figure:: graphics/gtec_calvalhyper_fig1.gif + :align: center + :alt: Hyperelastic Test Suite: Test Specimens + :figclass: align-center + + **Figure 15.1: Hyperelastic Test Suite: Test Specimens** + +The engineering-stress vs. engineering-strain results are as follows: + +.. figure:: graphics/gtec_calvalhyper_fig2.gif + :align: center + :alt: Hyperelastic Test Suite: Experimental Data + :figclass: align-center + :name: figure_experimental_data + + **Figure 15.2: Hyperelastic Test Suite: Experimental Data** + +The uniaxial specimen is similar to ASTM D412-C (ASTM Standard D412, 2006). + +The crosshead is displaced by 396 mm, giving a measured engineering strain in the +gage section of 662 percent and a calculated engineering stress of 58.1 MPa. + +The equibiaxial specimen is disc-shaped, with 16 equally spaced tabs about the +circumference. The tabs are stretched 127.3 mm, resulting in a measured engineering +strain in the gage section of 336 percent and a calculated engineering stress of +22.1 MPa. + +For the planar specimen, the crosshead is displaced by 191.6 mm, giving a +calculated engineering strain of 639 percent and a calculated engineering stress of +54.7 MPa. + +15.3.2. Validation Experiment +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +A simulated tension-torsion experiment was performed on a thin strip. The specimen +is similar to that specified in ASTM D1043 (ASTM Standard D1043, 2006) and is shown +here: + +.. figure:: graphics/gtec_calvalhyper_fig3.gif + :align: center + :alt: Tension-Torsion Test Specimen + :figclass: align-center + + **Figure 15.3: Tension-Torsion Test Specimen** + +The experiment consists of clamping each end of the specimen into the test +apparatus, then stretching the specimen by 50 percent of its original gage length +and twisting one end of the specimen for four complete revolutions. Following is the +resulting moment-vs.-rotation data: + +.. figure:: graphics/gtec_calvalhyper_fig4.gif + :align: center + :alt: Tension-Torsion Experimental Data + :figclass: align-center + + **Figure 15.4: Tension-Torsion Experimental Data** + +15.4. Analysis and Solution Controls +------------------------------------ + +Analysis and solution-control information for calibration and validation +follow: + +* `15.4.1. Calibrating Parameters`_ +* `15.4.2. Validating Parameters`_ + +15.4.1. Calibrating Parameters +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Material parameter calibration occurs using the curve-fitting +tool. + +**Example 15.1: Fitting a Hyperelastic Constitutive Model to a Set of Uniaxial Stress-Strain +Data** + +The command input shown here is for illustration only. While curve-fitting is +possible via command input, Ansys, Inc. recommends using the graphical user +interface (GUI) to perform the curve-fitting, or at least visually validating +the results using the GUI to ensure a sound fit. + +.. code:: apdl + + /PREP7 + TBFT,FADD,1,HYPER,MOONEY,3 + TBFT,EADD,1,UNIA,UNIAX.LOG + TBFT,SOLVE,1,HYPER,MOONEY,3 + TBFT,FSET,1,HYPER,MOONEY,3 + + + +The ``TBFT,FADD`` command initializes the curve-fitting procedure +for a hyperelastic, three-parameter, Mooney-Rivlin model assigned to +material identification number 1. + +``TBFT,EADD`` reads the uniaxial experimental data in the +``uniax.log`` file as the fitting data for material number 1. +The experimental data in the file is a set of engineering-strain vs. +engineering-stress input: + + +.. code:: output + + 0.819139E-01 0.82788577E+00 + 0.166709E+00 0.15437247E+01 + 0.253960E+00 0.21686152E+01 + 0.343267E+00 0.27201819E+01 + 0.434257E+00 0.32129833E+01 + 0.526586E+00 0.36589498E+01 + 0.619941E+00 0.40677999E+01 + 0.714042E+00 0.44474142E+01 + 0.808640E+00 0.48041608E+01 + 0.903519E+00 0.51431720E+01 + 0.998495E+00 0.54685772E+01 + 0.109341E+01 0.57836943E+01 + + +``TBFT,SOLVE`` determines the three constitutive parameters for the +Mooney-Rivlin model, minimizing the difference between the model and the +experimental data. + +``TBFT,FSET`` assigns the fitted constitutive parameters to +material number 1. + +For this problem, the fitted parameters for the three-parameter Mooney-Rivlin +model are: + ++----------------------------+ +| *`C`*10 =1.338856 | ++============================+ +| *`C`*11 = - 1.648364 x10-2 | ++----------------------------+ + + +15.4.2. Validating Parameters +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Following is a mesh developed to simulate the torsion experiment to validate the +fitted constitutive model parameters obtained in `15.4.1. Calibrating Parameters`_: + +.. figure:: graphics/gtec_calvalhyper_fig5.gif + :align: center + :alt: Tension-Torsion Test Specimen Mesh + :figclass: align-center + + **Figure 15.5: Tension-Torsion Test Specimen Mesh** + +The mesh consists of 1,332 SOLID186 elements using the +default formulation (a mixed-displacement pressure formulation with reduced +integration). + +The attachment of the test specimen +to the test apparatus is simulated by boundary conditions applied to the specimen in +the region of the clamps, as described here: + +* The back-left clamp region is fully restrained. +* The back-right clamp region is attached to a rigid-contact surface and + fixed in place. +* The front-left clamp region is attached to a rigid-contact surface and + displaced in the z direction to simulate a clamping displacement equal + to 25 percent of the specimen thickness. The same is true for the + front-right clamp region. + The stretching to 50 percent engineering strain is simulated by displacing the + rigid-contact surfaces attached to the right clamp regions while holding left clamp + regions fixed. + +The torsion of the specimen is simulated by holding the left clamp region in place +and twisting the keypoints attached to the right contact surfaces about the +longitudinal axis. + +15.5. Results and Discussion +---------------------------- + +Results for the calibration and validation operations are discussed below: + +* `15.5.1. Calibration Results`_ +* `15.5.2. Validation Results`_ + +15.5.1. Calibration Results +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Using all of experimental data shown in :numref:`figure_experimental_data` +to fit the three-, five-, and nine-parameter Mooney-Rivlin models results in the +following parameters, fit to the entire range of experimental data: + ++----------------+-------------------+------------------+------------------+ +| | Three-Parameter | Five-Parameter | Nine-Parameter | ++================+===================+==================+==================+ +| :math:`C_{10}` | 1.8785 | 1.4546 | 1.7095 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{01}` | -5.7759 x 10-2 | 7.6677 x 10-2 | 5.6365 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{20}` | --- | 1.3484 x 10-2 | -1.2088 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{11}` | 1.9589 x 10-3 | -4.4337 x 10-3 | 3.7099 x 10-5 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{02}` | --- | 2.3997 x 10-4 | -4.6858 x 10-4 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{30}` | --- | --- | 3.5202 x 10-4 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{21}` | --- | --- | 6.0562 x 10-6 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{12}` | --- | --- | 1.9666 x 10-5 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{03}` | --- | --- | -8.9997 x 10-7 | ++----------------+-------------------+------------------+------------------+ +| :math:`\nu` | 3.6415 | 3.0625 | 3.5318 | ++----------------+-------------------+------------------+------------------+ + +The following figure is a comparison of the models to the experimental data: + +.. figure:: graphics/gtec_calvalhyper_fig6.gif + :align: center + :alt: Comparison of the Data and Fits Over the Entire Range of Data + :figclass: align-center + + **Figure 15.6: Comparison of the Data and Fits Over the Entire Range of Data** + +Thus far, it is obvious that none of the models provide a suitable fit to the +entire range of experimental data. The reason is that the least-squares fitting +procedure is minimizing the error over the entire range of data; therefore, it can +be detrimental to include data that is not representative of the *actual range of use*. + +If the experimental data range is limited to about 100 percent strain, however, +the fitted parameters shown in the following table are obtained: + ++----------------+-------------------+------------------+------------------+ +| | Three-Parameter | Five-Parameter | Nine-Parameter | ++================+===================+==================+==================+ +| :math:`C_{10}` | 1.6540 | 1.7874 | 1.8904 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{01}` | 1.2929 x 10-1 | 5.7229 x 10-2 | -3.6352 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{20}` | --- | -5.8765 x 10-2 | -2.3484 x 10-1 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{11}` | -1.2726 x 10-2 | 2.6843 x 10-2 | 2.6511 x 10-1 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{02}` | --- | -5.1127 x 10-3 | -6.8670 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{30}` | --- | --- | 5.1742 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{21}` | --- | --- | -8.3262 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{12}` | --- | --- | 3.6204 x 10-2 | ++----------------+-------------------+------------------+------------------+ +| :math:`C_{03}` | --- | --- | -4.3754 x 10-3 | ++----------------+-------------------+------------------+------------------+ +| :math:`\nu` | 3.5665 | 3.6892 | 3.7081 | ++----------------+-------------------+------------------+------------------+ + +The following figure is a comparison of the models with the parameters fit to the +modified experimental data: + +.. figure:: graphics/gtec_calvalhyper_fig7.gif + :align: center + :alt: Parameters Fit to Experimental Data to About 100 Percent Strain + :figclass: align-center + + **Figure 15.7: Parameters Fit to Experimental Data to About 100 Percent Strain** + +For the equibiaxial and planar experiments, any of the three models might be +acceptable; however, the comparison with the uniaxial data might indicate that +*none* of the three models are acceptable. + +The behavior of the model outside the fitted range can significantly differ from +the actual response of the material. For example, the model parameters fit to the +experimental data to 100 percent strain have been used to simulate the hyperelastic +test suite to strains of about 200 percent, as shown in the following comparisons: + +.. figure:: graphics/gtec_calvalhyper_fig8.gif + :align: center + :alt: Comparison of the Data and Fits Showing Predictions Outside the Range of Fitted Data + :figclass: align-center + + **Figure 15.8: Comparison of the Data and Fits Showing Predictions Outside the Range of Fitted Data** + +Beyond 100 percent strain, it becomes apparent that some of the predictions +quickly deteriorate. In all three comparisons, the nine-parameter model quickly +loses accuracy, and it appears that the three- and nine-parameter Mooney-Rivlin +models have lost stability for the biaxial deformation case. + +15.5.2. Validation Results +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The five-parameter Mooney-Rivlin model, fit to the experimental data up to 100 +percent strain, is selected as an adequate representation of the material response. +The constitutive model is specified via the following input: + +.. code:: apdl + + C10 = 1.787381e+00 + C01 = 5.722875e-02 + C20 =-5.876502e-02 + C11 = 2.684331e-02 + C02 =-5.112790e-03 + TB,HYPER,1,,5,MOONEY + TBDATA,1,C10,C01,C20,C11,C02 + + +The following figure shows a contour plot of the strain energy density at the end +of simulation. The plot offers a general idea of the overall deformation of the +specimen. + +.. figure:: graphics/gtec_calvalhyper_fig9.gif + :align: center + :alt: Strain-Energy Density Contours of the Tension-Torsion Test + :figclass: align-center + + **Figure 15.9: Strain-Energy Density Contours of the Tension-Torsion Test** + +With the exception of the clamp regions, the deformation shows a uniform pattern +in the gage region along the axis of twisting. Perpendicular to the axis of twisting +is a large strain-energy density near the outside edge of the specimen, decreasing +toward the center. + +The following figure shows a comparison of the model with the experimental moment +vs. theta data: + +.. figure:: graphics/gtec_calvalhyper_fig10.gif + :align: center + :alt: Comparison of Tension-Torsion Experiment to the Five-Parameter Mooney-Rivlin Model + :figclass: align-center + + **Figure 15.10: Comparison of Tension-Torsion Experiment to the Five-Parameter Mooney-Rivlin Model** + +After a seemingly anomalous first data point, the error between the simulation and +experiment is in the range of 2 to 4 percent. Throughout the entire simulation, the +five-parameter Mooney-Rivlin model predicts a higher moment for an equivalent twist, +which is not entirely expected by the error plots for the hyperelastic test suite +comparisons; nevertheless, a maximum four percent error appears to be a reasonable +margin of error for this simulation. + +15.6. Recommendations +--------------------- + +When performing a similar type of calibration and validation, consider the following +recommendations: + +* Obtain test data from at least two (and preferably all three) of the + experiments in the hyperelastic test suite. +* Ensure that the test data covers the range of deformation over which the + constitutive model will be used. +* If the error between the experimental data and the constitutive model is too + great, try limiting the experimental data to the range of deformation over which + the constitutive model will be used. +* Use the constitutive model within the range of fitted data only. +* Use an independent experiment to validate that the constitutive model + adequately matches the material behavior. + +15.7. References +---------------- + +The following references were consulted when creating this example problem: + +1. ASTM International. (2006). (http://www.astm.org/Standards/D1043.htm). +*Standard Test Method for Stiffness Properties of Plastics as a Function of Temperature by Means of a Torsion Test*. +West Conshohocken. +2. ASTM International. (2006). [ASTM Standard D412](http://www.astm.org/Standards/D412.htm). +*Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers-Tension*. +West Conshohocken. + +15.8. Input Files +----------------- + +The following files were used in this problem: + +* **tension\_torsion.dat** -- Tension-torsion simulation input file. +* **tension\_torsion.cdb** -- The common database file containing the model information for this problem (called by +**tension\_torsion.dat** ). + ++-------------------------------------------------------------------------------------------------------------------------------------------+ +| `Download file set `_ | ++===========================================================================================================================================+ +| `Download all td-nn file sets in a single zip file. `_ | ++-------------------------------------------------------------------------------------------------------------------------------------------+ From a0f0de72f9899626746629c6739c4d1097332515 Mon Sep 17 00:00:00 2001 From: German Date: Mon, 9 Jan 2023 11:25:01 +0000 Subject: [PATCH 2/4] Fixing build warnings --- doc/source/conf.py | 3 ++ .../sphx_glr_tse-015-calvalhyper_thumb.gif | Bin 0 -> 35608 bytes .../technology_showcase_examples/index.rst | 27 ++++++++++++++++ ...lvalhyper.rst => ex-15-teccalvalhyper.rst} | 30 +++++++++--------- 4 files changed, 45 insertions(+), 15 deletions(-) create mode 100755 doc/source/technology_showcase_examples/images/thumb/sphx_glr_tse-015-calvalhyper_thumb.gif rename doc/source/technology_showcase_examples/techdemo-15/{p_ex_15-teccalvalhyper.rst => ex-15-teccalvalhyper.rst} (97%) diff --git a/doc/source/conf.py b/doc/source/conf.py index 4124e342c..aebd73987 100644 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -86,6 +86,9 @@ numpydoc_show_class_members = False numpydoc_xref_param_type = True +# Image referencing +numfig = True + # Consider enabling numpydoc validation. 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+ +.. raw:: html + + + +.. ######### + .. toctree:: :hidden: :includehidden: techdemo-1/ex_0-tecbrakesqueal + techdemo-15/ex-15-teccalvalhyper techdemo-20/ex_20-tecPCB techdemo-28/ex_28-tecfricstir diff --git a/doc/source/technology_showcase_examples/techdemo-15/p_ex_15-teccalvalhyper.rst b/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst similarity index 97% rename from doc/source/technology_showcase_examples/techdemo-15/p_ex_15-teccalvalhyper.rst rename to doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst index 15a55fdfd..4fddb07cb 100755 --- a/doc/source/technology_showcase_examples/techdemo-15/p_ex_15-teccalvalhyper.rst +++ b/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst @@ -146,13 +146,13 @@ possible via command input, Ansys, Inc. recommends using the graphical user interface (GUI) to perform the curve-fitting, or at least visually validating the results using the GUI to ensure a sound fit. -.. code:: apdl +.. code:: python3 - /PREP7 - TBFT,FADD,1,HYPER,MOONEY,3 - TBFT,EADD,1,UNIA,UNIAX.LOG - TBFT,SOLVE,1,HYPER,MOONEY,3 - TBFT,FSET,1,HYPER,MOONEY,3 + mapdl.prep7() + mapdl.tbft("fadd",1,"hyper","mooney",3) + mapdl.tbft("eadd",1,"unia","uniax".l)OG + mapdl.tbft("solve",1,"hyper","mooney",3) + mapdl.tbft("fset",1,"hyper","mooney",3) @@ -192,11 +192,11 @@ material number 1. For this problem, the fitted parameters for the three-parameter Mooney-Rivlin model are: -+----------------------------+ -| *`C`*10 =1.338856 | -+============================+ -| *`C`*11 = - 1.648364 x10-2 | -+----------------------------+ ++-----------------------------------+ +| :math:`C_{10} = 1.338856` | ++-----------------------------------+ +| :math:`C_{11} = - 1.648364 x10-2` | ++-----------------------------------+ 15.4.2. Validating Parameters @@ -360,8 +360,8 @@ The constitutive model is specified via the following input: C20 =-5.876502e-02 C11 = 2.684331e-02 C02 =-5.112790e-03 - TB,HYPER,1,,5,MOONEY - TBDATA,1,C10,C01,C20,C11,C02 + mapdl.tb("HYPER",1,"",5,"MOONEY") + mapdl.tbdata(1,C10,C01,C20,C11,C02) The following figure shows a contour plot of the strain energy density at the end @@ -432,8 +432,8 @@ West Conshohocken. The following files were used in this problem: * **tension\_torsion.dat** -- Tension-torsion simulation input file. -* **tension\_torsion.cdb** -- The common database file containing the model information for this problem (called by -**tension\_torsion.dat** ). +* **tension\_torsion.cdb** -- The common database file containing the model information for this problem + (called by **tension\_torsion.dat** ). +-------------------------------------------------------------------------------------------------------------------------------------------+ | `Download file set `_ | From ebdc4b96cc48ecf7c453962e302d38e4f759e4b6 Mon Sep 17 00:00:00 2001 From: German Date: Mon, 9 Jan 2023 11:25:20 +0000 Subject: [PATCH 3/4] changing code syntax --- .../techdemo-15/ex-15-teccalvalhyper.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst b/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst index 4fddb07cb..55ced5f9f 100755 --- a/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst +++ b/doc/source/technology_showcase_examples/techdemo-15/ex-15-teccalvalhyper.rst @@ -353,7 +353,7 @@ The five-parameter Mooney-Rivlin model, fit to the experimental data up to 100 percent strain, is selected as an adequate representation of the material response. The constitutive model is specified via the following input: -.. code:: apdl +.. code:: python3 C10 = 1.787381e+00 C01 = 5.722875e-02 From b9b44f5a9f8b2f23951b82261991e32bc6bd4555 Mon Sep 17 00:00:00 2001 From: German Date: Mon, 9 Jan 2023 12:42:34 +0000 Subject: [PATCH 4/4] Removing link to python file since it is not provided. --- doc/source/technology_showcase_examples/index.rst | 2 -- 1 file changed, 2 deletions(-) diff --git a/doc/source/technology_showcase_examples/index.rst b/doc/source/technology_showcase_examples/index.rst index 969280c22..8aa12e177 100644 --- a/doc/source/technology_showcase_examples/index.rst +++ b/doc/source/technology_showcase_examples/index.rst @@ -82,8 +82,6 @@ this project. .. image:: images/thumb/sphx_glr_tse-015-calvalhyper_thumb.gif :alt: Calibrating and Validating a Hyperelastic Constitutive Model - :ref:`sphx_glr_ex_15-teccalvalhyper.py` - .. raw:: html
Calibrating and Validating a Hyperelastic Constitutive Model