NOPE

Snippet Tmux configuration

2024-03-02T17:41:00+00:00

The configuration for tmux

bind h select-pane -L
bind j select-pane -D
bind k select-pane -U
bind l select-pane -R
setw -g mode-keys vi
set -sg escape-time 0

### use C-w to replace C-b
# bind  to C-w
# unbind C-b
# set-option -g prefix C-w
# bind-key C-w send-prefix

### use  s for horizontal split
bind s split-window -v

### use  v for vertical split
bind v split-window -h
bind -n M-Left select-pane -L
bind -n M-Right select-pane -R
bind -n M-Up select-pane -U
bind -n M-Down select-pane -D

### resize panes more easily
bind < resize-pane -L 10
bind > resize-pane -R 10
bind - resize-pane -D 10
bind + resize-pane -U 10

### force tmux to use 256 color
set -g default-terminal "screen-256color"

Snippet GDB cheat sheet

2024-02-17T09:30:15+00:00

The command for GDB debug

# Start GDB with a core file
gdb program corefile

# Show backtrace
bt

# Check local variables
info locals

# Check arguments
info args

# Navigate through stack frames
frame 1

# List the souce code
list

# Inspect memory
x/8x 0x12345678

# Step over
n

# Step into
s

# Step out
finish

# Quit
q

Key West, Florida

2023-12-18T17:10:21+00:00

Homemade laser power meter

2022-01-26T19:46:55+00:00

I made a simple laser power meter. The results are pretty good. I measured my own Uniphase helium-neon laser, the results show the laser power is around 0.68 to 0.70 mW. The value is consistent with the measured results from Coherent LaserCheck. The laser power meter consists of three parts: the photodiode, termination board, and circuit board. Here is the photo of this laser power meter.

The photodiode is SFH 206 K obtained from Newark. The photodiode is directly soldered on a small prototype PCB in the black box. I did not take a photo inside the black box before I used superglue to glue the box. The internal circuit is the recommended circuit from Thorlabs, as shown in the following figure. I use a 1k ohm resistor and 0.1 μF capacitor as the noise filter. The bias voltage and the termination resistor are wired out to the termination board.

Here is the detail of the termination board. There are several termination resistors that can be selected based on the position of the jump switch. If the frequency response does not matter, a large termination resistor can be selected so that the transimpedance amplifier can be saved. I use 10 resistors ranging from 50 ohms to 50k ohms. A large resistor such as 50k ohms here may not be necessary. I also put a small slide switch here. Therefore, the bias voltage for the photodiode can be selected either from the battery or the ESP32.

The signal is processed by a 16bit ADC (ADS1115) breakout board. ADS1115 communicates with ESP32 with the I2C protocol. The ESP32 is configured as an access point (AP) mode for the webserver. With AP mode, the router is not required here. I can directly connect to the Wi-Fi network sent by ESP32. ADS 1115 measures the voltage from the termination resistors and then the ESP32 calculates the laser power based on the measured voltage. The details will be given below.

Here are the webserver screenshots. Since the AP mode does not connect to the real Internet, the web server just provides the essential information here. Channel 2 is shorted with a jump, so the reading is zero here. Channel 1 reading is the measure of the ambient light. The channel configuration details are also provided. It can be seen that both channels are configured to measure the laser with a 633 nm wavelength. The configuration details can be changed on another page, as shown below. The change value will be saved in ESP 32 SPIFFS. So, the ESP 32 can store the values even after the restart.

The following section describes the calibration details. The photodiode calibration is based on the datasheet of SFH 206 K. The datasheet shows that the spectral sensitivity of the photodiode at 850 nm is 0.62 A/W. Also, the datasheet provides the relative spectral sensitivity curve, as shown below. Therefore, the sensitivity for each wavelength can be calculated.

I extract the data from the relative sensitivity curve and obtain the specific value at each wavelength.

Relative spectral sensitivity extract from the datasheet: Download
Power sensitivity with interpolation at each wavelength: Download

Therefore, with the value of termination resistors and the measured voltage from ADS 1115, the laser power can be calculated based on the above curve.

Abaqus UMAT environment troubleshooting

2021-10-05T15:05:05+00:00

During the subroutine environment setup, a lot of problems need to be solved. A typical problem is shown as following,

The job input file “Job-1.inp” has been submitted for analysis. Job Job-1: Analysis Input File Processor aborted due to errors. Error in job Job-1: Analysis Input File Processor exited with an error.

Such a problem can be figured out by checking the log file in the working directory. Here is the example of the “Job-1.log” in the working directory. The log file shows the “ifort” command cannot be recognized as an internal or external command. It means this command cannot be found in the system path. Actually, “ifort” is the command used to compile the Fortran file.

To solve the problem, we need to add the command path to the system path. First, I use the tool “Everything” to locate the file path.

Four results can be found in this tool. The second “ifort.exe” is located in an x64 folder which is the same as my Win 10. Then, copy the path of this folder and paste to the system path. Right-click ”This PC” and select the “Properties”,

Select “Advanced system settings”,

Select “Environment Variables…”,

Find the “Path” in “System variables”,

New an environment variable and paste the “ifort.exe” folder path into it,

Remember to RESTART the Abaqus after adding a new environment variable. In my Abaqus version (2018), the software cannot find the “ifort.exe” until I restart the software. Then, this problem is solved. But another problem occurs after I click the “submit” button.

When I check the “Job-1.dat” file, it shows the model is overconstrained. After I remove the constraint, the model can be compiled and run successfully.

Mathematica crack tip trajectory

2020-09-10T17:34:05+00:00

This post focuses on the crack tip tracking method. While I simulate several fatigue models, the crack tip trajectories are hard to track in the model. Previously, I just picked some points and decided on the crack length and rate in several images. This useful method is not very effective when I get several video clips in a crack place. Several image process tools such as Fiji can deal with the image fast and easily, but I still feel it is hard to realize my goal. So I try to write a simple tool to achieve the object. Since tracking the crack tip uses the technique of image processing, I use Mathematica for this purpose.

The main function used in Mathematica is the function called “ImageFeatureTrack”. This function will track some feature points in a sequence of images, and return the coordinates of these points in each image. Thus, the idea is not very difficult, we import the video and transfer it into the image sequence, then we specify the tracking points with the coordinates in the image and use ”ImageFeatureTrack” function to get the coordinates in each frame. The last step is to turn the image coordinates into the real model coordinates.

The first step is to import the file and turn it into a sequence of images. Additionally, the frame numbers are added to each frame to help inspect the image sequence,

(*Set up the path for a video file*)
fileInPath = NotebookDirectory[] <> "Crack.mov";
(*Import the file and get all frames*)
vIn = Import[fileInPath, {"Frames", All}];
(*Preview*)
vIn1 = Show[vIn[[#]], 
       Graphics[{Text[Style[#, FontSize -> 14], 
       Scaled[{.5, .8}]]}]] & /@
       Table[i, {i, Length[vIn]}];
ListAnimate[vIn1]

The last line uses the “ListAnimate” command to generate a generate animation in Mathematica,

Then, the tracking frame should be set according to the animation, in this example, the crack has a jump in 28th to 29th frame, so the frame number 29 should be used. At the end of the simulation, the crack becomes much more width, so I select more frames here,

trackFrame = {1, 29, 38, 42};
vIn1[[#]] & /@ trackFrame

The 1st, 29th, 38th, 42nd are shown to select the feature points here. Right-click the image and select Get Coordinates tool in the menu and pick the feature points on the image. Then use “Edit”->”Copy” to copy the coordinates. Since we chose four frames for tracking, four crack-tip feature points should be chosen. The following figure shows the point that I chose in the 29th frame.

Paste the coordinates into the following code,

trackCoord = {{335.9, 400.2}, {430.5, 406.1}, 
              {436.5, 410.6}, {444., 401.6}};
trackFrame1 = Append[trackFrame, Length[vIn] + 1];
trackFrame2 = Partition[trackFrame1, 2, 1];
trackFrame3 = ReplacePart[#, {-1} -> #[[-1]] - 1] & /@ trackFrame2;
rST = MapThread[
      ImageFeatureTrack[Take[vIn, #1], {#2}] &, {trackFrame3, 
      trackCoord}];
rST1 = Join @@ rST

The image coordinates of the crack tip will be stored in rST1,

Note that all these coordinates are just the image coordinates directly calculated from the image. Before we turn these coordinates into the real coordinates in the model, we should check the tracking quality. The method is very simple, I draw a small blue circle with the coordinates in “rST1” to each frame,

iMG1 = Table[ Show[vIn[[i]], 
       Graphics[{Blue, Thick, Circle[Flatten[rST1, 1][[i]], 5]}]], 
       {i, Length[vIn]}];
iMG2 = ImageResize[#, Scaled[1/1]] & /@ iMG1;

(*Add frame number to inspect the tracking results*)
iMG3 = Show[iMG2[[#]], 
       Graphics[{Text[Style[#, FontSize -> 14], Scaled[{.5, .8}]]}]] 
       & /@ Table[i, {i, Length[iMG2]}];
vOut = ListAnimate[iMG3]

Drag the slide bar to check the tracking quality. If Mathematica lost the tracking point, you should add more tracking frames in the previous code to correct the result. If the crack tip trajectory is tracked correctly, then the following code is used to transfer the image coordinates into the real coordinates in the model,

realCoord = {{4.79849, 1.83042}, {356.478, 359.281}};
imgCoord = {{81.77, 75.45}, {720.1, 724.5}};

(*Get the scale factor and origin position*)
realDist = realCoord[[2]] - realCoord[[1]];
imgDist = imgCoord[[2]] - imgCoord[[1]];
xyFactor = realDist/imgDist;
xyOrigin = xyFactor*(imgDist/realDist*(-realCoord[[1]]) + imgCoord[[1]]);
rST2 = xyFactor*# - xyOrigin & /@ Flatten[rST1, 1]

(*Draw the image coordinates*)
ListLinePlot[Flatten[rST1, 1], Mesh -> All]
ListLinePlot[rST2, Mesh -> All]

To calculate the real coordinates, I use the coordinates of two points. “realCoord” stores the real coordinates in the model, and “imgCoord” stores the coordinates in the image at the same model position. The result will be saved in rST2. Two list plots will be drawn to compare the coordinates,

The first figure is about the image coordinates and the second figure is the real coordinates in the model. Then, we export the animation.

fileOutPath = NotebookDirectory[] <> "Out.avi";
Export[fileOutPath, iMG2]

Here is the result animation:

Snippet Abaqus square plate inp

2020-05-02T17:34:05+00:00

An example to show the inp file structure. The example demonstrates the stretch of a square plate with the dimension $1 \times 1 \mathrm{m^2}$. The plate material is steel with elastic stiffness of $2.1 \times 10^{11} \mathrm{MPa}$. The material density is $7800 \mathrm{kg/m^3}$. The left boundary is fixed and $0.1 \mathrm{m}$ displacement is applied to the right boundary. The plane strain is assumed in the model. Here are the model and the simulation results.

The inp file is shown below,

*Heading
** Job name: Job-1 Model name: Model-1
** Generated by: Abaqus/CAE 2018
*Preprint, echo=NO, model=NO, history=NO, contact=NO
**
** PARTS
**
*Part, name=Part-1
*Node
      1,         -0.5,         -0.5
      2, -0.400000006,         -0.5
      3, -0.300000012,         -0.5
      4, -0.200000003,         -0.5
      5, -0.100000001,         -0.5
      6,           0.,         -0.5
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      8,  0.200000003,         -0.5
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     55,          0.5, -0.100000001
     56,         -0.5,           0.
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     60, -0.100000001,           0.
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     77,          0.5,  0.100000001
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     88,          0.5,  0.200000003
     89,         -0.5,  0.300000012
     90, -0.400000006,  0.300000012
     91, -0.300000012,  0.300000012
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     93, -0.100000001,  0.300000012
     94,           0.,  0.300000012
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     96,  0.200000003,  0.300000012
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     98,  0.400000006,  0.300000012
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    110,          0.5,  0.400000006
    111,         -0.5,          0.5
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    122, -0.449999988,         -0.5
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    156, -0.300000012, -0.350000024
    157, -0.350000024, -0.300000012
    158, -0.200000003, -0.350000024
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    161, -0.150000006, -0.300000012
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    286, -0.100000001,         0.25
    287, -0.150000006,  0.300000012
    288,           0.,         0.25
    289, -0.0500000007,  0.300000012
    290,  0.100000001,         0.25
    291, 0.0500000007,  0.300000012
    292,  0.200000003,         0.25
    293,  0.150000006,  0.300000012
    294,  0.300000012,         0.25
    295,         0.25,  0.300000012
    296,  0.400000006,         0.25
    297,  0.350000024,  0.300000012
    298,          0.5,         0.25
    299,  0.449999988,  0.300000012
    300, -0.400000006,  0.350000024
    301, -0.449999988,  0.400000006
    302,         -0.5,  0.350000024
    303, -0.300000012,  0.350000024
    304, -0.350000024,  0.400000006
    305, -0.200000003,  0.350000024
    306,        -0.25,  0.400000006
    307, -0.100000001,  0.350000024
    308, -0.150000006,  0.400000006
    309,           0.,  0.350000024
    310, -0.0500000007,  0.400000006
    311,  0.100000001,  0.350000024
    312, 0.0500000007,  0.400000006
    313,  0.200000003,  0.350000024
    314,  0.150000006,  0.400000006
    315,  0.300000012,  0.350000024
    316,         0.25,  0.400000006
    317,  0.400000006,  0.350000024
    318,  0.350000024,  0.400000006
    319,          0.5,  0.350000024
    320,  0.449999988,  0.400000006
    321, -0.400000006,  0.449999988
    322, -0.449999988,          0.5
    323,         -0.5,  0.449999988
    324, -0.300000012,  0.449999988
    325, -0.350000024,          0.5
    326, -0.200000003,  0.449999988
    327,        -0.25,          0.5
    328, -0.100000001,  0.449999988
    329, -0.150000006,          0.5
    330,           0.,  0.449999988
    331, -0.0500000007,          0.5
    332,  0.100000001,  0.449999988
    333, 0.0500000007,          0.5
    334,  0.200000003,  0.449999988
    335,  0.150000006,          0.5
    336,  0.300000012,  0.449999988
    337,         0.25,          0.5
    338,  0.400000006,  0.449999988
    339,  0.350000024,          0.5
    340,          0.5,  0.449999988
    341,  0.449999988,          0.5
*Element, type=CPE8R
  1,   1,   2,  13,  12, 122, 123, 124, 125
  2,   2,   3,  14,  13, 126, 127, 128, 123
  3,   3,   4,  15,  14, 129, 130, 131, 127
  4,   4,   5,  16,  15, 132, 133, 134, 130
  5,   5,   6,  17,  16, 135, 136, 137, 133
  6,   6,   7,  18,  17, 138, 139, 140, 136
  7,   7,   8,  19,  18, 141, 142, 143, 139
  8,   8,   9,  20,  19, 144, 145, 146, 142
  9,   9,  10,  21,  20, 147, 148, 149, 145
 10,  10,  11,  22,  21, 150, 151, 152, 148
 11,  12,  13,  24,  23, 124, 153, 154, 155
 12,  13,  14,  25,  24, 128, 156, 157, 153
 13,  14,  15,  26,  25, 131, 158, 159, 156
 14,  15,  16,  27,  26, 134, 160, 161, 158
 15,  16,  17,  28,  27, 137, 162, 163, 160
 16,  17,  18,  29,  28, 140, 164, 165, 162
 17,  18,  19,  30,  29, 143, 166, 167, 164
 18,  19,  20,  31,  30, 146, 168, 169, 166
 19,  20,  21,  32,  31, 149, 170, 171, 168
 20,  21,  22,  33,  32, 152, 172, 173, 170
 21,  23,  24,  35,  34, 154, 174, 175, 176
 22,  24,  25,  36,  35, 157, 177, 178, 174
 23,  25,  26,  37,  36, 159, 179, 180, 177
 24,  26,  27,  38,  37, 161, 181, 182, 179
 25,  27,  28,  39,  38, 163, 183, 184, 181
 26,  28,  29,  40,  39, 165, 185, 186, 183
 27,  29,  30,  41,  40, 167, 187, 188, 185
 28,  30,  31,  42,  41, 169, 189, 190, 187
 29,  31,  32,  43,  42, 171, 191, 192, 189
 30,  32,  33,  44,  43, 173, 193, 194, 191
 31,  34,  35,  46,  45, 175, 195, 196, 197
 32,  35,  36,  47,  46, 178, 198, 199, 195
 33,  36,  37,  48,  47, 180, 200, 201, 198
 34,  37,  38,  49,  48, 182, 202, 203, 200
 35,  38,  39,  50,  49, 184, 204, 205, 202
 36,  39,  40,  51,  50, 186, 206, 207, 204
 37,  40,  41,  52,  51, 188, 208, 209, 206
 38,  41,  42,  53,  52, 190, 210, 211, 208
 39,  42,  43,  54,  53, 192, 212, 213, 210
 40,  43,  44,  55,  54, 194, 214, 215, 212
 41,  45,  46,  57,  56, 196, 216, 217, 218
 42,  46,  47,  58,  57, 199, 219, 220, 216
 43,  47,  48,  59,  58, 201, 221, 222, 219
 44,  48,  49,  60,  59, 203, 223, 224, 221
 45,  49,  50,  61,  60, 205, 225, 226, 223
 46,  50,  51,  62,  61, 207, 227, 228, 225
 47,  51,  52,  63,  62, 209, 229, 230, 227
 48,  52,  53,  64,  63, 211, 231, 232, 229
 49,  53,  54,  65,  64, 213, 233, 234, 231
 50,  54,  55,  66,  65, 215, 235, 236, 233
 51,  56,  57,  68,  67, 217, 237, 238, 239
 52,  57,  58,  69,  68, 220, 240, 241, 237
 53,  58,  59,  70,  69, 222, 242, 243, 240
 54,  59,  60,  71,  70, 224, 244, 245, 242
 55,  60,  61,  72,  71, 226, 246, 247, 244
 56,  61,  62,  73,  72, 228, 248, 249, 246
 57,  62,  63,  74,  73, 230, 250, 251, 248
 58,  63,  64,  75,  74, 232, 252, 253, 250
 59,  64,  65,  76,  75, 234, 254, 255, 252
 60,  65,  66,  77,  76, 236, 256, 257, 254
 61,  67,  68,  79,  78, 238, 258, 259, 260
 62,  68,  69,  80,  79, 241, 261, 262, 258
 63,  69,  70,  81,  80, 243, 263, 264, 261
 64,  70,  71,  82,  81, 245, 265, 266, 263
 65,  71,  72,  83,  82, 247, 267, 268, 265
 66,  72,  73,  84,  83, 249, 269, 270, 267
 67,  73,  74,  85,  84, 251, 271, 272, 269
 68,  74,  75,  86,  85, 253, 273, 274, 271
 69,  75,  76,  87,  86, 255, 275, 276, 273
 70,  76,  77,  88,  87, 257, 277, 278, 275
 71,  78,  79,  90,  89, 259, 279, 280, 281
 72,  79,  80,  91,  90, 262, 282, 283, 279
 73,  80,  81,  92,  91, 264, 284, 285, 282
 74,  81,  82,  93,  92, 266, 286, 287, 284
 75,  82,  83,  94,  93, 268, 288, 289, 286
 76,  83,  84,  95,  94, 270, 290, 291, 288
 77,  84,  85,  96,  95, 272, 292, 293, 290
 78,  85,  86,  97,  96, 274, 294, 295, 292
 79,  86,  87,  98,  97, 276, 296, 297, 294
 80,  87,  88,  99,  98, 278, 298, 299, 296
 81,  89,  90, 101, 100, 280, 300, 301, 302
 82,  90,  91, 102, 101, 283, 303, 304, 300
 83,  91,  92, 103, 102, 285, 305, 306, 303
 84,  92,  93, 104, 103, 287, 307, 308, 305
 85,  93,  94, 105, 104, 289, 309, 310, 307
 86,  94,  95, 106, 105, 291, 311, 312, 309
 87,  95,  96, 107, 106, 293, 313, 314, 311
 88,  96,  97, 108, 107, 295, 315, 316, 313
 89,  97,  98, 109, 108, 297, 317, 318, 315
 90,  98,  99, 110, 109, 299, 319, 320, 317
 91, 100, 101, 112, 111, 301, 321, 322, 323
 92, 101, 102, 113, 112, 304, 324, 325, 321
 93, 102, 103, 114, 113, 306, 326, 327, 324
 94, 103, 104, 115, 114, 308, 328, 329, 326
 95, 104, 105, 116, 115, 310, 330, 331, 328
 96, 105, 106, 117, 116, 312, 332, 333, 330
 97, 106, 107, 118, 117, 314, 334, 335, 332
 98, 107, 108, 119, 118, 316, 336, 337, 334
 99, 108, 109, 120, 119, 318, 338, 339, 336
100, 109, 110, 121, 120, 320, 340, 341, 338
*Nset, nset=Set-1, generate
   1,  341,    1
*Elset, elset=Set-1, generate
   1,  100,    1
** Section: Section-1
*Solid Section, elset=Set-1, material=Material-1
1.,
*End Part
**  
**
** ASSEMBLY
**
*Assembly, name=Assembly
**  
*Instance, name=Part-1-1, part=Part-1
*End Instance
**  
*Nset, nset=Set-1, instance=Part-1-1
   1,  12,  23,  34,  45,  56,  67,  78
  89, 100, 111, 125, 155, 176, 197, 218
 239, 260, 281, 302, 323
*Elset, elset=Set-1, instance=Part-1-1, generate
  1,  91,  10
*Nset, nset=Set-2, instance=Part-1-1
  11,  22,  33,  44,  55,  66,  77,  88
  99, 110, 121, 151, 172, 193, 214, 235
 256, 277, 298, 319, 340
*Elset, elset=Set-2, instance=Part-1-1, generate
  10,  100,   10
*End Assembly
** 
** MATERIALS
** 
*Material, name=Material-1
*Density
7800.,
*Elastic
 2.1e+11, 0.3
** 
** BOUNDARY CONDITIONS
** 
** Name: BC-1 Type: Displacement/Rotation
*Boundary
Set-1, 1, 1
Set-1, 2, 2
Set-1, 6, 6
** ----------------------------------------------------------------
** 
** STEP: Step-1
** 
*Step, name=Step-1, nlgeom=NO
*Static
1., 1., 1e-05, 1.
** 
** BOUNDARY CONDITIONS
** 
** Name: BC-2 Type: Displacement/Rotation
*Boundary
Set-2, 1, 1, 0.1
** 
** OUTPUT REQUESTS
** 
*Restart, write, frequency=0
** 
** FIELD OUTPUT: F-Output-1
** 
*Output, field, variable=PRESELECT
** 
** HISTORY OUTPUT: H-Output-1
** 
*Output, history, variable=PRESELECT
*End Step

Software DeltaZ - Arbitrary waveform for RIGOL

2020-04-29T15:17:24+00:00

DeltaZ is a software to edit the arbitrary waveform on RIGOL DG800/900 series. I write some scripts to control my RIGOL DG812. Finally, I decided to pack the scripts and wrote a user interface to control the device. That is DeltaZ. Click the “DOWNLOAD” button to download the software.

Download and Installation

The software is compatible with Windows (x32, x64) platforms: DOWNLOAD

NI-VISA installation

The software needs NI-VISA runtime to communicate with RIGOL arbitrary waveform generator. Before the installation, please make sure the system has been licensed with the NI-VISA. If the LabView has been installed, NI-VISA should already be installed. Here are the steps to install NI-VISA runtime.

Google NI-VISA runtime and download the installer,

Install the NI Package Manager and open the manager. The NI-VISA runtime is needed for DeltaZ, so click “Deselect All” since we do not need the additional items. Then, click “Next”,

Accept the license agreements,

Review the installed module. “NI-VISA Runtime” is needed here,

Finish the installation.

DeltaZ

After installing the NI-VISA, Open the DeltaZ and connect it to the RIGOL 800/900 series with the “Device” tab. Click the “Refresh” button to refresh the devices. Click the “Connect” button to connect the device. If everything is correct, the “Connect” button should turn to Green.

The “Basic” tab provides the basic waveform, such as Sine, Square, Ramp, Pulse, Noise, and DC. The corresponding options are available based on the waveform type. Then, select the channel and click the “Download” button to download the waveform. Click the “Start” button to open the channel and output the waveform.

The second tab and third tab are used to define custom waveform. The “EasyEdit” tab is similar to the easy edit in ArbExpress. Drag the left cursor and right cursor with horizontal sliders to select the edit region. Click the “⯅” button and “⯆” button to change the amplitude of the selected region based on “VStep” value. The left cursor and right cursor can be adjusted by clicking the “⯇” button and “⯈” button. Use “L Cursor” and “R Cursor” to select the controlled cursor. “Manual Control” can be used to input a specific cursor position. Here is an example.

The “Cut”, “Copy” and “Paste” button can be used to edit the waveform between the two cursors. Here is an example.

The last “Advance” tab can be used to generate the waveform with math expression. The math expression supports all JavaScript math functions. Do not include the “Math” prefix before math function and each math function should end with parentheses, such as “random()”. Here is an example.

Disclaimer

I have put efforts into ensuring that the software works properly. Unfortunately, a full check of the software code cannot be ensured, despite my efforts, the function included in software could be functional. Therefore, the user should check the compatibility for software with the proper system, as the developer does not accept liability for any damage by using this software.

LAMMPS restart example

2020-04-20T13:13:22+00:00

LAMMPS has the capability to restart the job from the binary file. According to the description from the official website, the command restart can write out a binary restart file with the current state of the simulation every certain timestep. This command has two modes: write the binary file or the data file. If you wish to use the data file, then a convert command is needed in this scenario. Here we do not consider the data file.

This LAMMPS script is a simple stretch of an iron nanowire. The orientation of the iron nanowire is [100](001). Due to the simple orientation, this nanowire is constructed in the LAMMPS script file. The dimension of the nanowire is 20c in the x-direction, 10c in the y-direction and 10c in the z-direction, c is the lattice constant which is set to 2.856 in the script. Note that this lattice constant is just copied from Wikipedia. If you want more accurate data of the lattice constant, you can find on this website. The pair potential is the EAM potential from the LAMMPS internal potential library.

First, the entire system is needed to minimize the energy to get the equilibrium and rescale to 300K use the random velocity distribution. Then, a uniform strain is applied to the nanowire in the x-direction. The strain rate is maintained at 1E12 to save simulation time. Before running the simulation, the command restart 200 tmp.restart is inserted into the script, that means every 200 steps, a restart file will be written to the filesystem. Thus, we can restart this simulation with this restart binary file.

# Deforming a Si Nanowire.

# ------------------------ INITIALIZATION ----------------------------
units        metal
boundary     p s s
atom_style   atomic
neighbor 2.0 bin 
neigh_modify delay 5 every 1 

#------------ use LAMMPS to create Iron nanowire (for test) ------------ 
lattice bcc 2.856
region whole block -10 10 -5 5 -5 5 units lattice
create_box 1 whole
region LLF block -10 10 -5 5 -5 5 units lattice
lattice bcc 2.856 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
create_atoms 1 region LLF
mass 1 55.845
atom_modify sort 0 0.0

#----------------------- assign potential ----------------------------
pair_style eam/alloy 
pair_coeff * * Fe_mm.eam.fs Fe

# ------------------------- SETTINGS ---------------------------------
thermo 100 
velocity all create 300.0 12345
thermo_style custom step temp etotal press pxx pyy pzz lx ly lz vol

minimize 1.0e-4 1.0e-6 100 1000

#--------------------------- nve ensemble ----------------------------
reset_timestep 0 
timestep 0.001
fix 1 all nve
fix 2 all temp/rescale 1 300 300 1 0.1

variable timestep equal "step" 
variable temperature equal "temp" 
variable total_energy equal "etotal" 

dump 1 all custom 1000 equilibrate.lammpstrj id type x y z 

run 3000
unfix 1
unfix 2
undump 1

#------------Deform------------------------------
variable srate equal 1.0e11
variable srate1 equal "v_srate / 1.0e12"
fix 1 all deform 1 x erate ${srate1} remap x
fix 2 all nve
fix 3 all temp/rescale 1 300 300 1 0.1

variable tmp equal "lx"
variable L0 equal ${tmp}
variable p1 equal "(lx - v_L0)/v_L0"
variable p2 equal "-pxx/10000"
variable p3 equal "-pyy/10000"
variable p4 equal "-pzz/10000"
variable p5 equal "lx"
variable p6 equal "ly"
variable p7 equal "lz"
variable p8 equal "temp"
compute 1 all pe
compute 2 all ke

fix 4 all ave/time 1 20 100 v_p1 v_p2 c_1 c_2 file tension.dat
dump 1 all custom 100 tension.lammpstrj id type x y z 

restart  200 tmp.restart
run 2000 

After the simulation, get the restart file “tmp.restart.5000” and use the command read_restart in the restart script.

Note that the following commands do not need to be repeated because their settings are included in the restart file: units, atom_style, special_bonds, pair_style, bond_style. However these commands do need to be used since their settings are not in the restart file: neighbor, fix, timestep.

Actually, the pair_style and pair_coeff commands are still needed in the restart file, otherwise, LAMMPS will report . Here is the example of the restart file.

read_restart    tmp.restart.5000


neighbor 2.0 bin 
neigh_modify delay 5 every 1 

pair_style eam/alloy 
pair_coeff * * Fe_mm.eam.fs Fe

thermo 100 
thermo_style custom step temp etotal press pxx pyy pzz lx ly lz vol

timestep 0.001
variable srate equal 1.0e11
variable srate1 equal "v_srate / 1.0e12"
fix 1 all deform 1 x erate ${srate1} remap x
fix 2 all nve
fix 3 all temp/rescale 1 300 300 1 0.1

variable tmp equal "lx"
variable L0 equal ${tmp}
variable p1 equal "(lx - v_L0)/v_L0"
variable p2 equal "-pxx/10000"
variable p3 equal "-pyy/10000"
variable p4 equal "-pzz/10000"
variable p5 equal "lx"
variable p6 equal "ly"
variable p7 equal "lz"
variable p8 equal "temp"
compute 1 all pe
compute 2 all ke

fix 4 all ave/time 1 20 100 v_p1 v_p2 c_1 c_2 file tension.dat
dump 1 all custom 100 tension_restart.lammpstrj id type x y z 

run 2000

All source code is available upon request.

LAMMPS Plastic strain calculation

2020-04-20T13:13:22+00:00

This post provides the approach to extract the plastic strain in MD simulation. We can compute the atom displacement as the trajectory from the MD simulation, but the strain is the concept in continuum mechanics, it is really hard to compute the tensor in a discrete system. Recently, some tools provide this function based on a theory that accounting the effects of the neighbor atoms. While considering the relative displacement with the neighbor atom and using the weight function, the deformation gradient tensor can be calculated. Therefore, the strain tensor is obtained. Plastic strain can be expressed as,

\[\boldsymbol{\varepsilon}^p = \boldsymbol{\varepsilon} - \boldsymbol{\varepsilon}^e\]

so two strain tensor should be generated in the simulation data: total strain tensor $\boldsymbol{\varepsilon}$ and the elastic strain tensor $\boldsymbol{\varepsilon}^e$. Obviously, LAMMPS data file does not provide such information. Here I use the OVITO to get this data.

OVITO provide two modifiers, the first one is the “Atomic strain” and the second one is the “Elastic strain calculation”. Both of them provide the deformation gradient tensor and the strain tensor data. But I found there are some bugs for strain tensor output in OVITO, so I use the deformation gradient tensor data and computing the strain tensor with a Python script.

Let us start by running a Python script with the OVITO interpreter. Get into your OVITO installation folder and find the “ovitos.exe” in this directory. This is the Python interpreter. Actually, OVITO has integrated the Python interpreter, so we do not need to provide an extra Python interpreter. However, there is a drawback of this internal Python interpreter, the package in the internal interpreter just contains the “Numpy” and “Matplotlib”. So if you need the extra function from the Python package. I think you need just use the internal interpreter as the start.

The following image is from the official website of the OVITO documentation. If we get the object of the “ObjectNode”, then we can handle all data and modifiers in the pipeline.

Fortunately, the OVITO import_file function provides access to the “ObjectNode”. Now, we do some basic operations and define some functions before we try to get the deformation gradient tensors.

#Import several modules.
import os
import sys
import numpy as np
try:
    from ovito.io import * #Import the Ovito module
    from ovito.modifiers import *
except:
    pass

This part import several modules and try to import the “ovito.io” module. The Python script can just be run by the “ovitos.exe”, so use try except to avoid the error when running this script directly from the interpreter.

The first function is to form the Voigt notation to a matrix form. You can get more information about the Ovigt notation from the Wikipedia here. In general, since several tensors, such as the stress tensors, strain tensor and stiffness tensor, have symmetric properties, Voigt notation simplifies the expression to a vector to reduce the computational cost. For example, If we get the principal strain tensor and use Voigt notation to express them, the plastic flow rule can be simplified. Here is the matForm function,

def matForm(voigtM):
    if type(voigtM) is not np.ndarray: #check the type of voigtM
        sys.exit("matForm: the parameter should be ")
    elif voigtM.ndim != 1: #check the dim of voigtM
        sys.exit("matForm: the parameter should be 1 dimension")
    outputM = np.zeros(shape=(3,3))
    if len(voigtM) == 6: # strain tensor
        outputM[0,0] = voigtM[0]
        outputM[1,1] = voigtM[1]
        outputM[2,2] = voigtM[2]
        outputM[0,1] = voigtM[3]
        outputM[0,2] = voigtM[4]
        outputM[1,2] = voigtM[5]
        outputM[1,0] = voigtM[3]
        outputM[2,0] = voigtM[4]
        outputM[2,1] = voigtM[5]
    if len(voigtM) == 9: #Deformation gradient tensor
        outputM[0,0] = voigtM[0]
        outputM[1,0] = voigtM[1]
        outputM[2,0] = voigtM[2]
        outputM[0,1] = voigtM[3]
        outputM[1,1] = voigtM[4]
        outputM[2,1] = voigtM[5]
        outputM[0,2] = voigtM[6]
        outputM[1,2] = voigtM[7]
        outputM[2,2] = voigtM[8]
    return outputM

Note that the order in OVITO is different from that of the traditional Voigt notation. Usually, Voigt notation treats the order of a strain tensor as,

\[\left( \varepsilon_{11}, \varepsilon_{22}, \varepsilon_{33}, \varepsilon_{23}, \varepsilon_{13}, \varepsilon_{12} \right)\]

but in OVITO, the order will be,

\[\left( \varepsilon_{11}, \varepsilon_{22}, \varepsilon_{33}, \varepsilon_{12}, \varepsilon_{13}, \varepsilon_{23} \right)\]

Then, the following functions define the Almansi tensor and Green tensor,

def almansiStrain(defGradM):
    almansiStrain = np.zeros(shape=(3,3)) #Start a empty matrix
    identityM = np.identity(3) #Set the identity matrix
    # Get the rank of defGradM
    if np.linalg.matrix_rank(defGradM) != 3: 
        return almansiStrain
    try:
        invdefGradM = np.linalg.inv(defGradM)
    except np.linalg.LinAlgError:
        # Not invertible. Skip this one.almansiStrain
        return almansiStrain
    else:
        almansiStrain = 1.0 / 2.0 * (identityM - \
                        np.dot(np.transpose(invdefGradM),invdefGradM))
    return almansiStrain

def greenStrain(defGradM):
    greenStrain = np.zeros(shape=(3,3))
    identityM = np.identity(3)
    greenStrain = 1.0 / 2.0 * (np.dot(np.transpose(defGradM),\
                  defGradM) - identityM)
    return greenStrain

Green tensor can be written as,

\[{\bf E} = {1 \over 2} \left( {\bf F}^T \cdot {\bf F} - {\bf I} \right)\]

and Almansi tesnor is,

\[{\bf e} = \frac{1}{2} ({\bf I} - {\bf F}^{-T} \! \cdot {\bf F}^{-1})\]

The defination can be found in the continuum mechanics website.

After both elastic strain tensor and the total strain tensor are obtained from the calculation, the plastic strain tensor should be,

def plasticStrain(elasticDefGrad, totalDefGrad):
    #Compute the plastic strain tensor: totalStrain - elasticStrain
    elasticAlmansiStrain = almansiStrain(matForm(elasticDefGrad))
    totalAlmansiStrain = almansiStrain(matForm(totalDefGrad))
    plasticAlmansiStrain = totalAlmansiStrain - elasticAlmansiStrain
    return plasticAlmansiStrain

The last thing here is to turn the matrix form to Ovigt notation since we need to save the plastic strain tensor,

def matStrainToLine(mat):
    voigtForm = np.empty((1,6), float)
    voigtForm[0,0] = mat[0,0]
    voigtForm[0,1] = mat[1,1]
    voigtForm[0,2] = mat[2,2]
    voigtForm[0,3] = mat[0,1]
    voigtForm[0,4] = mat[0,2]
    voigtForm[0,5] = mat[1,2]
    return voigtForm

Now, let us set the working directory and the main function,

#######################################################
#Set the parameters
#######################################################
#Set file path.
workDir = "/Users/zhudongping/Documents/Research/Item2/"
inputFileName = "tension.lammpstrj"
outputFrameSeq = list(range(0,85,5))+list(range(3,85,5))
#outputFrameSeq = [43]
atomCutOffDist = 5.5
atomLatticeConst = 2.8665
try:
    atomLatticeType = ElasticStrainModifier.Lattice.BCC
except:
    pass
if __name__ == '__main__':
    try:
        main()
    except:
        print('=================ATTENTION===================')
        print('Please run this script with Ovito interpreter')
        print('=============================================')

All source code is available upon request.