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achalhp 2024-04-09 11:56:43 +05:30
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.ipynb_checkpoints/Twin_reorientation_check-checkpoint.ipynb Normal file
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Twin_reorientation_check.ipynb
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@ -5,8 +5,10 @@
"id": "e2ae546c-570b-4245-99fa-60519f448e1e", "id": "e2ae546c-570b-4245-99fa-60519f448e1e",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# Code to verify and visualize Reorientation by Correspondence Matrix\n", "# Code to verify and visualize reorientation caused twinning in the deformation gradient.\n",
"## Using the correspondence matrix method.\n",
"By Satyapriya Gupta, Achal H P\n", "By Satyapriya Gupta, Achal H P\n",
"\n",
"Reference Niewczas, Acta Materialia, 2010" "Reference Niewczas, Acta Materialia, 2010"
] ]
}, },
@ -111,7 +113,7 @@
"id": "1262386a-1d9c-4bb0-a147-c409f45ec751", "id": "1262386a-1d9c-4bb0-a147-c409f45ec751",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Initial Undeformed Condition, F = Identity matrix" "### Initial Undeformed Condition, $ F = Identity matrix $"
] ]
}, },
{ {
@ -129,7 +131,7 @@
"id": "64b46853-7012-432f-93c1-4acb1fe4dc9a", "id": "64b46853-7012-432f-93c1-4acb1fe4dc9a",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### If F = I, then inverse of F gives Fe." "### If $F = I$, then inverse of $F$ gives $F_e$."
] ]
}, },
{ {
@ -208,7 +210,7 @@
"id": "d21c31d5-72b1-43ed-91e4-2b194cd4eaaf", "id": "d21c31d5-72b1-43ed-91e4-2b194cd4eaaf",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Right polar decomposition of Fe, $ F_e = R U $ gives the rotation of deformed voxel." "### Right polar decomposition of $F_e$, $ F_e = R U $ gives the rotation of deformed voxel."
] ]
}, },
{ {
@ -339,8 +341,10 @@
"source": [ "source": [
"# Code to visualization of lattice reorientation caused by twinning.\n", "# Code to visualization of lattice reorientation caused by twinning.\n",
"\n", "\n",
"First cell below gives HCP unit cell with euler angles 0,0,0\n", "First cell below gives HCP unit cell with euler angles 0,0,0.\n",
"\n",
"Second cell below rotates unit cell by provided euler angles.\n", "Second cell below rotates unit cell by provided euler angles.\n",
"\n",
"Third cell below shows reorientation done after twinning." "Third cell below shows reorientation done after twinning."
] ]
}, },