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Commit c5472f9d authored by Dmitri Naumov's avatar Dmitri Naumov
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Merge branch 'PLLC_model_update' into 'master' 

[MFront] PLLC model update

See merge request ogs/ogs!4283
parents 5b192cef 963821d4
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MaterialLib/SolidModels/MFront/PowerLawLinearCreep.mfront
+ 11
− 14
View file @ c5472f9d
......@@ -8,7 +8,7 @@ model for salt creep. Bérest et al. (2019). Rock Mech Rock Eng.
@Algorithm NewtonRaphson;
@MaximumNumberOfIterations 100;
@Epsilon 1.e-14;
@Epsilon 1.e-12;
@Theta 1.0;
@ModellingHypotheses{".+"};
......@@ -51,23 +51,20 @@ Ru.setEntryName("UniversalGasConstant");
@Integrator
{
const auto s = deviator(sig);
const auto norm_s = sigmaeq(sig) / std::sqrt(3. / 2.);
const auto norm_s = std::max(sigmaeq(sig),1e-14*mu) / std::sqrt(3. / 2.);
constexpr auto Pdev = Stensor4::K();
const auto bPL = std::pow(3. / 2., (m + 1) / 2) * A1 *
std::exp(-Q1 / Ru / (T + dT)) / std::pow(sig0, m);
const auto bL = 3. / 2. * A2 / std::pow(Dgrain, 3) *
const auto bL = 3. / 2. * A2 / (std::pow(Dgrain, 3) * (T + dT)) *
std::exp(-Q2 / Ru / (T + dT)) / sig0;
if (norm_s > 1e-14 * mu)
{
const auto norm_s_pow = std::pow(norm_s, m - 1);
depsPL = dt * bPL * norm_s_pow * s;
depsL = dt * bL * s;
feel += depsPL + depsL;
dfeel_ddeel +=
2. * mu * dt *
(bPL * norm_s_pow * (Pdev + (((m - 1) / norm_s / norm_s) * s ^ s)) +
bL * Pdev);
}
const auto norm_s_pow = std::pow(norm_s, m - 1);
depsPL = dt * bPL * norm_s_pow * s;
depsL = dt * bL * s;
feel += depsPL + depsL;
dfeel_ddeel +=
2. * mu * dt *
(bPL * norm_s_pow * (Pdev + (((m - 1) / norm_s / norm_s) * s ^ s)) +
bL * Pdev);
}
ProcessLib/SmallDeformation/Tests.cmake
+ 4
− 0
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......@@ -95,6 +95,7 @@ if (OGS_USE_MFRONT)
if(NOT OGS_USE_MPI)
OgsTest(PROJECTFILE Mechanics/GuentherSalzer/model_triaxtest.prj)
endif()
OgsTest(PROJECTFILE Mechanics/PLLC/uniax_compression.prj)
# Linear elastic, no internal state variables, no external state variables.
AddTest(
......@@ -266,4 +267,7 @@ if(NOT OGS_USE_PETSC)
if(NOT WIN32)
NotebookTest(NOTEBOOKFILE Mechanics/Linear/DiscWithHole/Linear_Disc_with_hole_convergence_analysis.ipynb RUNTIME 40)
endif()
if (OGS_USE_MFRONT)
NotebookTest(NOTEBOOKFILE Mechanics/PLLC/PLLC.ipynb RUNTIME 7)
endif()
endif()
Tests/Data/Mechanics/PLLC/PLLC.ipynb 0 → 100644
+ 231
− 0
View file @ c5472f9d
%% Cell type:raw id:bb0907b4-4e26-4c4e-ab1f-22b5330cb1d2 tags:
title = "Power Law Linear Creep"
date = "2023-01-02"
author = "Florian Zill"
notebook = "Mechanics/PLLC/PLLC.ipynb"
web_subsection = "small-deformations"
<!--eofm-->
%% Cell type:markdown id:fa8cd9b5 tags:
### Power Law Linear Creep
This benchmark shows the increased creep rate of salt rock at lower deviatoric stress. A two component power law (which we call Power Law Linear Creep, or short PLLC) provides an easy way to capture the power law behaviour (dislocation creep) and the linear behaviour (pressure solution creep). For more details have a look at (Zill et al., 2022).
%% Cell type:code id:7962f42f-fd53-4fc1-b966-a8ba924aca6c tags:
``` python
import contextlib
import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
import os
import vtuIO
from ogs6py import ogs
prj_name = "uniax_compression"
data_dir = os.environ.get('OGS_DATA_DIR', str(os.getcwd()).split("/Data/")[0] + "/Data/")
input_file = f"{data_dir}/Mechanics/PLLC/{prj_name}.prj"
out_dir = os.environ.get('OGS_TESTRUNNER_OUT_DIR', f'{data_dir}/Mechanics/PLLC/_out')
if not os.path.exists(out_dir):
os.makedirs(out_dir)
os.chdir(out_dir)
prj_file = f"{out_dir}/{prj_name}_out.prj"
ogs_model = ogs.OGS(INPUT_FILE=input_file, PROJECT_FILE=prj_file)
```
%% Cell type:markdown id:7250c5b0 tags:
### Experimental data
A nice overview for the strain rates of salt for different temperatures and differential stresses can be found in (Li et al., 2021).
%% Cell type:code id:5a20a14e tags:
``` python
# Unfortunately the source for the WIPP data has gone missing - will be added if it's found again
ExData = {
"WIPP CS 25": (25, "^", [[9.87970002, 2.013560846E-05], [11.84642707, 3.178356756E-05], [7.87388785, 1.66059726E-06]]),
"WIPP CS 60": (60, "^", [[3.98589289, 5.7824853E-06], [5.94266985, 2.075776623E-05], [7.87388785, 1.953209818E-05], [9.96978837, 5.841438703E-05], [11.84642707, 0.00011762092257], [13.94911482, 0.00026749321794], [17.9857158, 0.00111804208073], [1.9814251, 8.7645834E-07], [3.91418422, 4.01350889E-06], [5.88897108, 3.34371363E-06], [7.87388785, 1.129440706E-05], [9.87970002, 2.99068674E-05], [11.84642707, 7.681792203E-05], [13.82306874, 0.00011067584933], [15.83934389, 0.00052247037957]]),
"DeVries 1988 25": (25, "s", [[4.99, 2.10816E-06], [4.99, 2.4192E-06], [5, 1.8144E-06], [9.99, 2.2032E-05], [14.96, 9.2448E-05], [14.98, 0.000216]]),
"DeVries 1988 100": (100, "s", [[4.95, 9.6768E-05], [6.77, 0.000292896], [7.46, 0.000324], [8.55, 0.000664416], [8.92, 0.00091584], [8.98, 0.0009936], [9.91, 0.00124416], [10.1, 0.00139968], [10.22, 0.00093312], [10.27, 0.00132192], [12.1, 0.00216], [12.3, 0.00409536], [12.35, 0.00320544], [12.37, 0.00292032], [12.39, 0.00253152], [12.4, 0.0026784], [12.46, 0.0025056], [12.49, 0.00347328], [13.57, 0.00273024], [13.78, 0.00242784], [14.7, 0.00482112], [16.87, 0.0095904], [17.2, 0.0123552], [19.96, 0.030672]]),
"DeVries 1988 200": (200, "s", [[3.47, 0.00117504], [4.71, 0.0032832], [6.67, 0.0104544], [6.78, 0.0132192], [9.86, 0.214272]]),
"Berest 2015 14.3": (14.3, "P", [[0.09909639, 8.944207E-08], [0.19575886, 1.4118213E-07], [0.29452325, 1.4118213E-07], [0.49411031, 9.799173E-08]]),
"Berest 2017 7.8": (7.8, "P", [[0.19575886,2.2285256E-07], [0.19575886,9.505469E-08], [0.19754389,2.5947583E-07], [0.19754389,2.647936E-08], [0.39379426,4.9162047E-07], [0.39738509,6.801413E-08], [0.59247161,4.0957628E-07], [0.59247161,5.7241269E-07], [0.59787408,1.0735864E-07], [1.0591736,1.11804208E-06]])}
```
%% Cell type:markdown id:6d38a65c tags:
### Parameters
This set of parameters gives a good fit with the experimental data. The grain size is a bit larger than the usual grain size of roughly 1 cm.
%% Cell type:code id:8066a6d3 tags:
``` python
A1 = 0.18 # d^-1
Q1 = 54e3 # kJ / mol
A2 = 6.5e-5 # m^3 K d^−1
Q2 = 24.5e3 # kJ / mol
dGrain = 5e-2 # m
sref = 1. # MPa
BGRa = lambda sig, T: A1 * np.exp(-Q1/(8.3145*(273.15+T))) * np.power(sig/sref,5.)
PLLC = lambda sig, T: A1 * np.exp(-Q1/(8.3145*(273.15+T))) * np.power(sig/sref,5.) + \
A2 * np.exp(-Q2/(8.3145*(273.15+T))) * sig/sref / np.power(dGrain, 3) / (273.15+T)
```
%% Cell type:markdown id:f1e5ec96 tags:
### Simulation and plot
The experimental data is compared against the model results (analytically and numerically)
%% Cell type:code id:7e2e294c-e803-4f02-b5ab-9bdfef94b00f tags:
``` python
lo_stresses = np.array([0.2e6, 0.6e6])
hi_stresses = np.array([2e6, 10e6])
Exps = {7.8: ('blue', lo_stresses), 14.3: ('orange', lo_stresses),
25: ('lime', hi_stresses), 60: ('red', hi_stresses),
100: ('gray', hi_stresses), 200: ('mediumpurple', hi_stresses)}
fig, ax = plt.subplots(1, 1, figsize=(8, 6))
ax.set_xlabel('$\\sigma_\\mathrm{ax}$ / MPa')
ax.set_ylabel('$\\dot{\\epsilon}_{zz}$ / d$^{-1}$')
ax.set_xlim(0.15, 30)
ax.set_ylim(1e-15, 1e1)
ax.grid(visible=True, which='both')
points = {'pt0': (1., 1., 1.)}
sigs = np.logspace(-1, 2, 100)
for temp, (col, stresses) in Exps.items():
# plot analytical curves
if temp >= 25:
ax.plot(sigs, BGRa(sigs, temp), color=col, ls='--')
ax.plot(sigs, PLLC(sigs, temp), color=col, ls='-')
# simulation in ogs and plot results
eps_dot = []
ogs_model.replace_parameter_value("T_ref", str(temp + 273.15))
for stress in stresses:
ogs_model.replace_parameter_value("sigma_ax", str(-stress))
ogs_model.write_input()
# hide output
with contextlib.redirect_stdout(None):
ogs_model.run_model(logfile=f"{out_dir}/out.txt",
args="-m " + f"{data_dir}/Mechanics/PLLC/")
pvdfile = vtuIO.PVDIO(f"{prj_name}.pvd", dim=3)
eps_zz = pvdfile.read_time_series("epsilon", points)["pt0"][:, 2]
eps_zz_dot = np.abs(np.diff(eps_zz)) / np.diff(pvdfile.timesteps)
# omit the first timestep
eps_dot += [np.mean(eps_zz_dot[1:])]
ax.loglog(1e-6*stresses, eps_dot, 'o', c=col, markeredgecolor="k")
# plot experimental data points
for Ex, (temp, m, Data) in ExData.items():
stresses, eps_dot = np.array(Data).T
ax.loglog(stresses, eps_dot, m, c=Exps[temp][0])
# create legend
patches = [mpl.patches.Patch(color=col, label=str(temp) + '°C')
for temp, (col, _) in Exps.items() if temp >= 25][::-1]
addLeg = lambda **args : patches.append(mpl.lines.Line2D([], [], **args))
addLeg(c='k', label='PLLC')
addLeg(c='k', ls='--', label='BGRa')
addLeg(c='w', ls='None', marker='o', mec="k", label='OGS')
addLeg(c='k', ls='None', marker='s', label='DeVries (1988)')
addLeg(c='k', ls='None', marker='^', label='WIPP CS')
addLeg(c='b', ls='None', marker='P', label='Bérest (2017) 7.8°C')
addLeg(c='orange', ls='None', marker='P', label='Bérest (2015) 14.3°C')
ax.legend(handles=patches, loc='best')
fig.tight_layout()
plt.show()
```
%% Cell type:markdown id:05f56358 tags:
### References
Zill, Florian, Wenqing Wang, and Thomas Nagel. Influence of THM Process Coupling and Constitutive Models on the Simulated Evolution of Deep Salt Formations during Glaciation. The Mechanical Behavior of Salt X. CRC Press, 2022. https://doi.org/10.1201/9781003295808-33.
Li, Shiyuan, and Janos Urai. Numerical Studies of the Deformation of Salt Bodies with Embedded Carbonate Stringers. Online, print. Publikationsserver der RWTH Aachen University, 2012. http://publications.rwth-aachen.de/record/211523/files/4415.pdf
Tests/Data/Mechanics/PLLC/cube_1x1x1.gml 0 → 100644
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<?xml version="1.0" encoding="ISO-8859-1"?>
<?xml-stylesheet type="text/xsl" href="OpenGeoSysGLI.xsl"?>
<OpenGeoSysGLI xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ogs="http://www.opengeosys.org">
<name>cube_1x1x1_geometry</name>
<points>
<point id="0" x="0" y="0" z="0"/>
<point id="1" x="0" y="0" z="1"/>
<point id="2" x="0" y="1" z="1"/>
<point id="3" x="0" y="1" z="0"/>
<point id="4" x="1" y="0" z="0"/>
<point id="5" x="1" y="0" z="1"/>
<point id="6" x="1" y="1" z="1"/>
<point id="7" x="1" y="1" z="0"/>
</points>
<surfaces>
<surface id="0" name="left"><!-- x=0 -->
<element p1="0" p2="1" p3="2"/>
<element p1="0" p2="3" p3="2"/>
</surface>
<surface id="1" name="right"><!-- x=1 -->
<element p1="4" p2="6" p3="5"/>
<element p1="4" p2="6" p3="7"/>
</surface>
<surface id="2" name="top"><!-- z=1 -->
<element p1="1" p2="2" p3="5"/>
<element p1="5" p2="2" p3="6"/>
</surface>
<surface id="3" name="bottom"><!-- z=0 -->
<element p1="0" p2="3" p3="4"/>
<element p1="4" p2="3" p3="7"/>
</surface>
<surface id="4" name="front"><!-- y=0 -->
<element p1="0" p2="1" p3="4"/>
<element p1="4" p2="1" p3="5"/>
</surface>
<surface id="5" name="back"><!-- y=1 -->
<element p1="2" p2="3" p3="6"/>
<element p1="6" p2="3" p3="7"/>
</surface>
</surfaces>
</OpenGeoSysGLI>
Tests/Data/Mechanics/PLLC/cube_1x1x1_hex_1e0.vtu 0 → 100644
+ 33
− 0
View file @ c5472f9d
<?xml version="1.0"?>
<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian" compressor="vtkZLibDataCompressor">
<UnstructuredGrid>
<Piece NumberOfPoints="8" NumberOfCells="1">
<PointData>
</PointData>
<CellData>
</CellData>
<Points>
<DataArray type="Float64" Name="Points" NumberOfComponents="3" format="binary" RangeMin="0" RangeMax="1.7320508076">
AQAAAACAAADAAAAAHAAAAA==eJxjYMAHPtjjlcaQh/GJ1YdLPy51mDQAp2EONQ==
</DataArray>
</Points>
<Cells>
<DataArray type="Int64" Name="connectivity" format="binary" RangeMin="0" RangeMax="7">
AQAAAACAAABAAAAAHgAAAA==eJxjYIAARijNDKWZoDQLlGaF0uxQmg1KAwAC8AAd
</DataArray>
<DataArray type="Int64" Name="offsets" format="binary" RangeMin="8" RangeMax="8">
AQAAAACAAAAIAAAACwAAAA==eJzjYIAAAABIAAk=
</DataArray>
<DataArray type="UInt8" Name="types" format="binary" RangeMin="12" RangeMax="12">
AQAAAACAAAABAAAACQAAAA==eJzjAQAADQAN
</DataArray>
<DataArray type="Int64" Name="faces" format="binary" RangeMin="0" RangeMax="0">
AQAAAACAAAAIAAAACwAAAA==eJxjYIAAAAAIAAE=
</DataArray>
<DataArray type="Int64" Name="faceoffsets" format="binary" RangeMin="1" RangeMax="1">
AQAAAACAAAAIAAAACwAAAA==eJxjZIAAAAAQAAI=
</DataArray>
</Cells>
</Piece>
</UnstructuredGrid>
</VTKFile>
Tests/Data/Mechanics/PLLC/uniax_compression.prj 0 → 100644
+ 240
− 0
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<?xml version="1.0" encoding="ISO-8859-1"?>
<OpenGeoSysProject>
<mesh>cube_1x1x1_hex_1e0.vtu</mesh>
<geometry>cube_1x1x1.gml</geometry>
<processes>
<process>
<name>SD</name>
<type>SMALL_DEFORMATION</type>
<integration_order>2</integration_order>
<constitutive_relation>
<type>MFront</type>
<behaviour>PowerLawLinearCreep</behaviour>
<material_properties>
<material_property name="YoungModulus" parameter="E"/>
<material_property name="PoissonRatio" parameter="nu"/>
<material_property name="PowerLawFactor" parameter="A"/>
<material_property name="PowerLawEnergy" parameter="Q"/>
<material_property name="PowerLawExponent" parameter="n"/>
<material_property name="ReferenceStress" parameter="sigma_f"/>
<material_property name="LinearLawFactor" parameter="A2"/>
<material_property name="LinearLawEnergy" parameter="Q2"/>
<material_property name="SaltGrainSize" parameter="Dgrain"/>
</material_properties>
</constitutive_relation>
<solid_density>rho_sr</solid_density>
<specific_body_force>0 0 0</specific_body_force>
<reference_temperature>T_ref</reference_temperature>
<process_variables>
<process_variable>displacement</process_variable>
</process_variables>
<secondary_variables>
<secondary_variable internal_name="ElasticStrain" output_name="ElasticStrain"/>
<secondary_variable internal_name="sigma" output_name="sigma"/>
<secondary_variable internal_name="epsilon" output_name="epsilon"/>
</secondary_variables>
</process>
</processes>
<time_loop>
<processes>
<process ref="SD">
<nonlinear_solver>basic_newton</nonlinear_solver>
<convergence_criterion>
<type>DeltaX</type>
<norm_type>NORM2</norm_type>
<abstol>1e-12</abstol>
</convergence_criterion>
<time_discretization>
<type>BackwardEuler</type>
</time_discretization>
<time_stepping>
<type>FixedTimeStepping</type>
<t_initial>0</t_initial>
<t_end>2</t_end>
<timesteps>
<pair>
<repeat>1</repeat>
<delta_t>1</delta_t>
</pair>
</timesteps>
</time_stepping>
</process>
</processes>
<output>
<type>VTK</type>
<prefix>uniax_compression</prefix>
<timesteps>
<pair>
<repeat>1</repeat>
<each_steps>1</each_steps>
</pair>
</timesteps>
<variables>
<variable>displacement</variable>
<variable>sigma</variable>
<variable>epsilon</variable>
<variable>ElasticStrain</variable>
</variables>
<suffix>_ts_{:timestep}_t_{:time}</suffix>
</output>
</time_loop>
<parameters>
<parameter>
<name>T_ref</name>
<type>Constant</type>
<value>298.15</value>
</parameter>
<parameter>
<name>E</name>
<type>Constant</type>
<value>25e9</value>
</parameter>
<parameter>
<name>nu</name>
<type>Constant</type>
<value>0.25</value>
</parameter>
<parameter>
<name>A</name>
<type>Constant</type>
<value>0.18</value>
</parameter>
<parameter>
<name>n</name>
<type>Constant</type>
<value>5.0</value>
</parameter>
<parameter>
<name>sigma_f</name>
<type>Constant</type>
<value>1e6</value>
</parameter>
<parameter>
<name>Q</name>
<type>Constant</type>
<value>54000</value>
</parameter>
<parameter>
<name>A2</name>
<type>Constant</type>
<value>6.5e-5</value>
</parameter>
<parameter>
<name>Q2</name>
<type>Constant</type>
<value>24500</value>
</parameter>
<parameter>
<name>Dgrain</name>
<type>Constant</type>
<value>5e-2</value>
</parameter>
<parameter>
<name>rho_sr</name>
<type>Constant</type>
<value>2570.0</value>
</parameter>
<parameter>
<name>displacement0</name>
<type>Constant</type>
<values>0 0 0</values>
</parameter>
<parameter>
<name>sigma_ax</name>
<type>Constant</type>
<value>-1e6</value>
</parameter>
<parameter>
<name>zero</name>
<type>Constant</type>
<value>0</value>
</parameter>
</parameters>
<process_variables>
<process_variable>
<name>displacement</name>
<components>3</components>
<order>1</order>
<initial_condition>displacement0</initial_condition>
<boundary_conditions>
<boundary_condition>
<geometrical_set>cube_1x1x1_geometry</geometrical_set>
<geometry>left</geometry>
<type>Dirichlet</type>
<component>0</component>
<parameter>zero</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>cube_1x1x1_geometry</geometrical_set>
<geometry>front</geometry>
<type>Dirichlet</type>
<component>1</component>
<parameter>zero</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>cube_1x1x1_geometry</geometrical_set>
<geometry>bottom</geometry>
<type>Dirichlet</type>
<component>2</component>
<parameter>zero</parameter>
</boundary_condition>
<boundary_condition>
<geometrical_set>cube_1x1x1_geometry</geometrical_set>
<geometry>top</geometry>
<type>Neumann</type>
<component>2</component>
<parameter>sigma_ax</parameter>
</boundary_condition>
</boundary_conditions>
</process_variable>
</process_variables>
<nonlinear_solvers>
<nonlinear_solver>
<name>basic_newton</name>
<type>Newton</type>
<max_iter>100</max_iter>
<linear_solver>general_linear_solver</linear_solver>
</nonlinear_solver>
</nonlinear_solvers>
<linear_solvers>
<linear_solver>
<name>general_linear_solver</name>
<eigen>
<solver_type>SparseLU</solver_type>
<scaling>true</scaling>
</eigen>
</linear_solver>
</linear_solvers>
<test_definition>
<vtkdiff>
<file>uniax_compression_ts_2_t_2.000000.vtu</file>
<field>displacement</field>
<absolute_tolerance>1e-13</absolute_tolerance>
<relative_tolerance>1e-14</relative_tolerance>
</vtkdiff>
<vtkdiff>
<file>uniax_compression_ts_2_t_2.000000.vtu</file>
<field>NodalForces</field>
<absolute_tolerance>1e-9</absolute_tolerance>
<relative_tolerance>1e-11</relative_tolerance>
</vtkdiff>
<vtkdiff>
<file>uniax_compression_ts_2_t_2.000000.vtu</file>
<field>sigma</field>
<absolute_tolerance>1e-8</absolute_tolerance>
<relative_tolerance>1e-12</relative_tolerance>
</vtkdiff>
<vtkdiff>
<file>uniax_compression_ts_2_t_2.000000.vtu</file>
<field>epsilon</field>
<absolute_tolerance>1e-14</absolute_tolerance>
<relative_tolerance>1e-15</relative_tolerance>
</vtkdiff>
<vtkdiff>
<file>uniax_compression_ts_2_t_2.000000.vtu</file>
<field>ElasticStrain</field>
<absolute_tolerance>1e-14</absolute_tolerance>
<relative_tolerance>1e-15</relative_tolerance>
</vtkdiff>
</test_definition>
</OpenGeoSysProject>
Tests/Data/Mechanics/PLLC/uniax_compression_ts_2_t_2.000000.vtu 0 → 100644
+ 37
− 0
View file @ c5472f9d
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