[cig-commits] [commit] add_thermodynamic_potentials: Added new VRH and HS bound benchmarks (8b9fb89)
cig_noreply at geodynamics.org
cig_noreply at geodynamics.org
Tue Dec 9 15:37:24 PST 2014
Repository : https://github.com/geodynamics/burnman
On branch : add_thermodynamic_potentials
Link : https://github.com/geodynamics/burnman/compare/86159898b81d2060d54a5610273ccb842c727eaf...8b9fb89bc6a4ecfef8ceaffb61e81e8da56c09ef
>---------------------------------------------------------------
commit 8b9fb89bc6a4ecfef8ceaffb61e81e8da56c09ef
Author: Bob Myhill <myhill.bob at gmail.com>
Date: Tue Dec 9 15:36:43 2014 -0800
Added new VRH and HS bound benchmarks
>---------------------------------------------------------------
8b9fb89bc6a4ecfef8ceaffb61e81e8da56c09ef
.../input_figures/Avseth_et_al_2010_fig3_K.png | Bin 0 -> 149499 bytes
.../input_figures/Hashin_Shtrikman_1963_fig1_K.png | Bin 0 -> 43826 bytes
.../input_figures/Hashin_Shtrikman_1963_fig2_G.png | Bin 0 -> 52707 bytes
.../input_figures/Hashin_Shtrikman_1963_fig3_E.png | Bin 0 -> 63529 bytes
tests/benchmark.py | 160 +++++++++++++++++++--
5 files changed, 146 insertions(+), 14 deletions(-)
diff --git a/burnman/data/input_figures/Avseth_et_al_2010_fig3_K.png b/burnman/data/input_figures/Avseth_et_al_2010_fig3_K.png
new file mode 100644
index 0000000..e57ffbf
Binary files /dev/null and b/burnman/data/input_figures/Avseth_et_al_2010_fig3_K.png differ
diff --git a/burnman/data/input_figures/Hashin_Shtrikman_1963_fig1_K.png b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig1_K.png
new file mode 100644
index 0000000..24b6d9c
Binary files /dev/null and b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig1_K.png differ
diff --git a/burnman/data/input_figures/Hashin_Shtrikman_1963_fig2_G.png b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig2_G.png
new file mode 100644
index 0000000..50300e1
Binary files /dev/null and b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig2_G.png differ
diff --git a/burnman/data/input_figures/Hashin_Shtrikman_1963_fig3_E.png b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig3_E.png
new file mode 100644
index 0000000..211a63f
Binary files /dev/null and b/burnman/data/input_figures/Hashin_Shtrikman_1963_fig3_E.png differ
diff --git a/tests/benchmark.py b/tests/benchmark.py
index f060601..6bc1aec 100644
--- a/tests/benchmark.py
+++ b/tests/benchmark.py
@@ -380,10 +380,16 @@ def check_averaging():
#these values are not given in the paper, so far as I can tell,
#so I did my best to read them off of the figure...
- K1=0.27
- K2=1.00
- G1=0.07
- G2=1.00
+
+
+ # MgO bulk and shear moduli
+ K2=180. # Bulk modulus, GPa
+ G2=155. # Shear modulus, GPa
+
+ # AgCl bulk and shear moduli (estimated from plot)
+ G1=G2*0.07
+ K1=K2*0.27
+
for i in range(len(volumes)):
v_bulk_modulus[i] = voigt.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
@@ -403,11 +409,11 @@ def check_averaging():
fig = mpimg.imread('../burnman/data/input_figures/watt_1976_a1.png')
plt.imshow(fig, extent=[0,1.0,0.25,1.0], aspect='auto')
- plt.plot(volumes, v_bulk_modulus, 'g-')
- plt.plot(volumes, r_bulk_modulus, 'g-')
- plt.plot(volumes, vrh_bulk_modulus, 'g-')
- plt.plot(volumes, hsu_bulk_modulus, 'g-')
- plt.plot(volumes, hsl_bulk_modulus, 'g-')
+ plt.plot(volumes, v_bulk_modulus/K2, 'g-')
+ plt.plot(volumes, r_bulk_modulus/K2, 'g-')
+ plt.plot(volumes, vrh_bulk_modulus/K2, 'g-')
+ plt.plot(volumes, hsu_bulk_modulus/K2, 'g-')
+ plt.plot(volumes, hsl_bulk_modulus/K2, 'g-')
plt.ylim(0.25,1.00)
plt.xlim(0,1.0)
plt.xlabel("Volume fraction")
@@ -417,11 +423,11 @@ def check_averaging():
fig = mpimg.imread('../burnman/data/input_figures/watt_1976_a2.png')
plt.imshow(fig, extent=[0,1.0,0.0,1.0], aspect='auto')
- plt.plot(volumes, v_shear_modulus, 'g-')
- plt.plot(volumes, r_shear_modulus, 'g-')
- plt.plot(volumes, vrh_shear_modulus, 'g-')
- plt.plot(volumes, hsu_shear_modulus, 'g-')
- plt.plot(volumes, hsl_shear_modulus, 'g-')
+ plt.plot(volumes, v_shear_modulus/G2, 'g-')
+ plt.plot(volumes, r_shear_modulus/G2, 'g-')
+ plt.plot(volumes, vrh_shear_modulus/G2, 'g-')
+ plt.plot(volumes, hsu_shear_modulus/G2, 'g-')
+ plt.plot(volumes, hsl_shear_modulus/G2, 'g-')
plt.ylim(0.0,1.00)
plt.xlim(0,1.0)
plt.xlabel("Volume fraction")
@@ -453,8 +459,134 @@ def check_averaging():
plt.show()
+
+def check_averaging_2():
+ """
+ Reproduce Figure 1 from Hashin and Shtrikman (1963) to check the
+ Hashin-Shtrikman bounds for an elastic composite
+ """
+
+ hashin_shtrikman_upper = burnman.averaging_schemes.HashinShtrikmanUpper()
+ hashin_shtrikman_lower = burnman.averaging_schemes.HashinShtrikmanLower()
+
+ #create arrays for sampling in volume fraction
+ volumes = np.linspace(0.0,1.0,100)
+ hsu_bulk_modulus = np.empty_like(volumes)
+ hsu_shear_modulus = np.empty_like(volumes)
+ hsl_bulk_modulus = np.empty_like(volumes)
+ hsl_shear_modulus = np.empty_like(volumes)
+
+
+ #These values are from the paper
+ K1=25.0
+ K2=60.7
+ G1=11.5
+ G2=41.8
+
+ for i in range(len(volumes)):
+ hsu_bulk_modulus[i] = hashin_shtrikman_upper.average_bulk_moduli( [1.0-volumes[i], volumes[i]], [K1,K2], [G1,G2] )
+ hsu_shear_modulus[i] = hashin_shtrikman_upper.average_shear_moduli( [1.0-volumes[i], volumes[i]], [K1,K2], [G1,G2] )
+
+ hsl_bulk_modulus[i] = hashin_shtrikman_lower.average_bulk_moduli( [1.0-volumes[i], volumes[i]], [K1,K2], [G1,G2] )
+ hsl_shear_modulus[i] = hashin_shtrikman_lower.average_shear_moduli( [1.0-volumes[i], volumes[i]], [K1,K2], [G1,G2] )
+
+ fig = mpimg.imread('../burnman/data/input_figures/Hashin_Shtrikman_1963_fig1_K.png')
+ plt.imshow(fig, extent=[0,1.0,1.1,K2+0.3], aspect='auto')
+ plt.plot(volumes, hsu_bulk_modulus, 'g-')
+ plt.plot(volumes, hsl_bulk_modulus, 'g-')
+ plt.ylim(K1,K2)
+ plt.xlim(0,1.0)
+ plt.xlabel("Volume fraction")
+ plt.ylabel("Averaged bulk modulus")
+ plt.title("Comparing with Figure 1 of Hashin and Shtrikman (1963)")
+ plt.show()
+
+ fig = mpimg.imread('../burnman/data/input_figures/Hashin_Shtrikman_1963_fig2_G.png')
+ plt.imshow(fig, extent=[0,1.0,0.3,G2], aspect='auto')
+ plt.plot(volumes, hsu_shear_modulus, 'g-')
+ plt.plot(volumes, hsl_shear_modulus, 'g-')
+ plt.ylim(G1,G2)
+ plt.xlim(0,1.0)
+ plt.xlabel("Volume fraction")
+ plt.ylabel("Averaged shear modulus")
+ plt.title("Comparing with Figure 2 of Hashin and Shtrikman (1963)")
+ plt.show()
+
+def check_averaging_3():
+ """
+ Reproduce Figure 3 from Avseth et al. (2010) to check the Voigt, Reuss,
+ Voigt-Reuss-Hill, and Hashin-Shtrikman bounds for an elastic composite
+ """
+ voigt = burnman.averaging_schemes.Voigt()
+ reuss = burnman.averaging_schemes.Reuss()
+ voigt_reuss_hill = burnman.averaging_schemes.VoigtReussHill()
+ hashin_shtrikman_upper = burnman.averaging_schemes.HashinShtrikmanUpper()
+ hashin_shtrikman_lower = burnman.averaging_schemes.HashinShtrikmanLower()
+
+ #create arrays for sampling in volume fraction
+ volumes = np.linspace(0.0,1.0,100)
+ v_bulk_modulus = np.empty_like(volumes)
+ v_shear_modulus = np.empty_like(volumes)
+ r_bulk_modulus = np.empty_like(volumes)
+ r_shear_modulus = np.empty_like(volumes)
+ vrh_bulk_modulus = np.empty_like(volumes)
+ vrh_shear_modulus = np.empty_like(volumes)
+ hsu_bulk_modulus = np.empty_like(volumes)
+ hsu_shear_modulus = np.empty_like(volumes)
+ hsl_bulk_modulus = np.empty_like(volumes)
+ hsl_shear_modulus = np.empty_like(volumes)
+ hs_av_bulk_modulus = np.empty_like(volumes)
+ hs_av_shear_modulus = np.empty_like(volumes)
+
+
+ # Quartz bulk and shear moduli
+ K2=37.
+ G2=45.
+
+ # Fluid bulk and shear moduli
+ G1=0.00001
+ K1=2.35
+
+
+ for i in range(len(volumes)):
+ v_bulk_modulus[i] = voigt.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+ v_shear_modulus[i] = voigt.average_shear_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+
+ r_bulk_modulus[i] = reuss.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+ r_shear_modulus[i] = reuss.average_shear_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+
+ vrh_bulk_modulus[i] = voigt_reuss_hill.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+ vrh_shear_modulus[i] = voigt_reuss_hill.average_shear_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+
+ hsu_bulk_modulus[i] = hashin_shtrikman_upper.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+ hsu_shear_modulus[i] = hashin_shtrikman_upper.average_shear_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+
+ hsl_bulk_modulus[i] = hashin_shtrikman_lower.average_bulk_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+ hsl_shear_modulus[i] = hashin_shtrikman_lower.average_shear_moduli( [volumes[i], 1.0-volumes[i]], [K1,K2], [G1,G2] )
+
+ hs_av_bulk_modulus[i] = 0.5*hsl_bulk_modulus[i] + 0.5*hsu_bulk_modulus[i]
+ hs_av_shear_modulus[i] = 0.5*hsl_shear_modulus[i] + 0.5*hsu_shear_modulus[i]
+
+ fig = mpimg.imread('../burnman/data/input_figures/Avseth_et_al_2010_fig3_K.png')
+ plt.imshow(fig, extent=[0,1.0,0.,40.0], aspect='auto')
+ plt.plot(volumes, v_bulk_modulus, 'g-')
+ plt.plot(volumes, r_bulk_modulus, 'g-')
+ plt.plot(volumes, vrh_bulk_modulus, 'g-')
+ plt.plot(volumes, hsu_bulk_modulus, 'g-')
+ plt.plot(volumes, hsl_bulk_modulus, 'g-')
+ plt.plot(volumes, hs_av_bulk_modulus, 'g-')
+ plt.ylim(0.,40.00)
+ plt.xlim(0.,1.0)
+ plt.xlabel("Volume fraction")
+ plt.ylabel("Averaged bulk modulus")
+ plt.title("Comparing with Figure 3 of Avseth et al., 2010")
+ plt.show()
+
+
if __name__ == "__main__":
check_averaging()
+ check_averaging_2()
+ check_averaging_3()
check_birch_murnaghan()
check_slb_fig7()
check_slb_fig3()
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