107 lines
4.9 KiB
Markdown
107 lines
4.9 KiB
Markdown
# Computational micromechanics of bioabsorbable magnesium stents
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Journal Article: https://doi.org/10.1016/j.jmbbm.2014.01.007
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Supporting Data - including original software versions: https://zenodo.org/records/11184080
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If you don't have access to the paper the content is very similar to that in my thesis section 5.4, available for download at: https://researchrepository.universityofgalway.ie/entities/publication/6168a11d-5962-4e52-97d1-6f2684a97ac2
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# Running simulations
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## Abaqus User Material ##
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The Abaqus UMAT `UCrys_HCP_Only.for` is used for the simulations in the paper.
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In the UMAT we assume a cartesian `GLOBAL` axis for the overall problem and a cartesian `LOCAL` axis to define the orientation of the crystal. Via input properties (`PROPS`) 3-5 and 6-8 we specify the directions of the `LOCAL` x and y axes in the `GLOBAL` coordinate system, assuming an orthogonal `LOCAL` z axis given by the cross-product with 'right hand rule'.
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A sample input file `MATERIAL` specification is shown for the UMAT:
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```
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*MATERIAL, NAME=MATERIAL-1
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**
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*USER MATERIAL, CONSTANTS=22, UNSYMM
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45000.,0.3,1.,0.,0.,0.,0.,1.
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4.,1.,0.,10.,20.,150.,7500.,40.,
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260.,7500.,5.,200.,0.11,10.
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*Depvar
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163
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*
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```
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which sets the 22 input properties. These propeties are as follows:
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``` fortran
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c PROPS
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c 1) Elastic Modulus
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c 2) Poisson's ratio
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c 3) x-axis orientaion in GLOBAL, x-coord
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c 4) x-axis orientation in GLOBAL, y-coord
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c 5) x-axis orientation in GLOBAL, z-coord
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c 6) y-axis orientation in GLOBAL, x-coord
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c 7) y-axis orientation in GLOBAL, y-coord
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c 8) y-axis orientation in GLOBAL, z-coord
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c 9) Crystal type: 1-4. FCC=1, HCP=2,3,4 (+Pyr, +Twin)
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c 10) Initial slip system strength FCC or HCP Basal
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c 11) FCC Hardening param
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c 12) FCC/HCp Basal hardening param
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c 13) Initial slip system strength HCP Prismatic
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c 14) Prismatic hardening param
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c 15) Prismatic hardening param
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c 16) Initial slip system strength HCP Pyramidal
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c 17) Pyramidal hardening param
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c 18) Pyramidal hardening param
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c 19) Initial slip system strength HCP Twin
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c 20) Twin system hardening param
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c 21) Twin system hardening param
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c 22) Twin system hardening param
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c
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```
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## Channel Die Simulations ##
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The channel die simulations described in the paper use `CDIE_1E.inp` as an input file.
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Loading and constraint directions are described via [Miller-Bravais](https://en.wikipedia.org/wiki/Miller_index) indices, which are (informally) a way to describe directions in the crystal lattice, and can be regarded as the inverted intersection coordinates of planes described in crystal-specific coordinate systems.
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For the HCP material here four axes are used, three (`a_1`, `a_2`, `a_3`) are on one of the crystal basal planes with equal angles between them (120 degrees) and the fourth (`c`) is normal to the basal plane. Thus we have three coordinate systems in total:
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* the HCP lattice system via MB indices
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* the cartesian crystal local `LOCAL` system
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* the `GLOBAL` system.
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In the simulated experiment the die is always closed in the `GLOBAL` (negative) z direction via this boundary condition in the INP file:
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```
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** Name: BC-4 Type: Displacement/Rotation
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*Boundary, amplitude=Amp-1
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Set-2, 1, 1, -1.
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```
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while another direction allows the the material to freely deform (`GLOBAL` x or y, not sure which).
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To replicate the series of channel die simulations, with loading and constraint directions shown in the table below:
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| Simulation | Load Direction | Constraint Direction |
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| --- | --- | --- |
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| A | `[0001]` | `[101^0]` |
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| B | `[0001]` | `[12^10]` |
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| C | `[101^0]` | `[0001]` |
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| D | `[12^10]` | `[0001]` |
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| E | `[101^0]` | `[12^10]` |
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| F | `[12^10]` | `[101^1]` |
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we thus need to determine suitable crystal input orientation parameters for each test, so that the crystal is loaded and constrainted accoring to the described Miller-Bravais indices.
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### Determing UMAT properties for crystal orientation ###
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Taking the first case as an example, load direction `[0 0 0 1]` means the loading will happen along the `c` axis of the crystal (or perpendicular to the basal plane). This contrains the crystal local `x` and `y` axes to be normal to the global `z` direction `(0, 0, 1)`.
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The constraint direction `[1 0 1_bar 0]` is on a plane that intercepts the hcp crystal 'a_1' axis at '1' and its 'a_3' axis at '-1'. Assuming the a_1 axis is equivalent to the crystal local x-axis, then the a_3 axis is a 240 degree rotation around the crystal local z-axis. Moving in the negative direction on the a_3 axis corresponds to a (240-180=) 60 degree rotation around the z axis, and talking the midway point (since we are moving 1 and -1 along each axis) means a 30 degree rotation about 'z'. Thus, if we want to constrain the crystal in the `[1 0 1_bar 0]` direction relative to a global constraint in the x direction we would need to rotate it by -30 degrees about the global z.
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