BMPRegion Command

An advanced feature of both NairnMPM and NairnFEA is that you can digitize objects directly from images.

Introduction

An alternative method for creating meshes in NairnFEA or material points in NairnMPM to to create them from an image file. The image file can be one you draw in a CAD program or can be a photo of object. The later options lets you create realistic numerical models of complex objects in a single command. In 2D or axisymmetric calculations, the image fills in an FEA mesh or adds material points to the grid. in 3D MPM simulations, the image represents one slice of the object in the x-y plane at a fixed value of z. By combining a stack of slices, those images can create all material points for a complex 3D object.

BMPRegion Commands

The command to digitize images is the same for both FEA and MPM input files. In scripted files, an image is converted into material points using:

BMPRegion (bmpPath),(width),<(height)>,<(scheme)>,<(anglesPath)>,...
  Origin (xO),(yO),<(zO>,<(flip)>
  Intensity (matID),(grayMin),(grayMax),<(prop),(value)>,...
    . . .
  Intensity "angles",(gray1),(gray2),(angle1),(angle2)
  (optional rotation command - MPM only)
EndRegion

In XML files, the command block is (must be within the single <MaterialPoints> element for MPM input files):

<BMP name="(bmpPath)" width="(width)" height="(height)" anglesZ="(anglesPath)" anglesY="(anglesPath)" anglesX="(anglesPath)">
  <Origin x="(xO)" y="(yO)" z="(zO)" flipped="(flip)"/>
  <Intensity mat="(matID)" imin="(gramMin)" imax="(grayMax)">
     (property command options)
  </Intensity>
    . . .
  <Intensity imin="(gray1)" imax="(gray2)" minAngle="(angle1)" maxAngle="(angle2)"/>
  (optional rotation commands - MPM only)
</BMP>

where

• (bmpPath) is the full or relative path name to the BMP file. The file must be an uncompressed, gray-scale, BMP file with 8 or less bits per pixel. The most useful is an 8-bit file with 256 levels of gray.
• (width) and (height) specify the width and height for the image, but there are several ways to specify them.
• (scheme) specfies are rotation scheme if BMP files are provided to determine those angles. The scheme must by "Z" for 2D simulations (all rotations are about the z axis) or can be any one axis (X, Y, or Z), and pair of axes (e.g., "XY"), or any three axis scheme beginning in Z (e.g., "ZYZ"). The (scheme) must be followed by one (anglesPath) for each axis in the scheme. Because 2D simulations must always be "Z", the (scheme) can be omitted and replaced with the one (anglesPath).
• (anglesPath),... are 1 to 3 (one for each axis defined in (scheme)) optional full or relative path names to BMP files whose intensities determine a material angle for rotation about the corresponding axis in (scheme) (or z axis if (scheme) is omitted). The angles can set Euler angles to orient the material axes at the start of simulations with anisotropic materials. The files must be an uncompressed, gray-scale, BMP files with 8 or less bits per pixel. The file must be exactly the same size (horizontal and vertical pixels) as the image file in (bmpPath). The gray scale values are mapped to angles by using Intensity commands. The relation of axes to Euler angles determine the initial rotation matrix for each particle.

Note that XML files do not use the (scheme) argument. Instead, the option angle files are set with anglesZ, anglesY, and anglesX attributes. These attributes can set 1 to 3 files in 3D, but can only set anglesZ in 2D. The order of the attributes determines the (scheme) (for backward compatibility, the attribute (angles) is equivalent to (anglesZ)).

Inside BMPRegion block, you include various commands to determine how the pixels are converted into material points. The possible subordinate commands are:

• Origin command - used to connected the image coordinates the the MPM grid coordinates.
• Intensity command - used to determine conversion of gray scale values in the images into material points or rotation angles
• (optional rotation commands) - these optional commands provide alternative methods for setting initial material orientation when modeling with anisotropic materials, but are only allowed in MPM input files.

Image Width and Height

The (width) and (height) parameters specify the width and height of the image, but they can be specified using different styles. The options are:

1. Give both as positive numbers - if both numbers are provided and are positive, they give width and height of the image in length units (or determined by a units attribute in XML files). They need not match the aspect ratio of actual image, but if they differ the image will be scaled.
2. Use a negative number - if either (width) or (height) is negative, the absolute value is taken as the number of length units per pixel (or other units per pixel as determined by a units attribute in XML files). The total width or height is calculated from the number of pixels in the BMP image.
3. Give only one dimension - if only (width) or only (height) are given, the entered parameter gives that dimension of the image in length units, if positive, or length units per pixel, if negative (or other units as determined by a units attribute in XML files). The other dimension is calculated from the aspect ratio of the BMP file. To specify only (height) in scripted files, the (width) parameter has to be more negative than -1e8. To specify only (width) in scripted files that are using the optional (anglesPath) parameter, the (height) parameter has to be more negative than -1e8.

Origin Command

The Origin command within a BMPRegion block (or <BMP> element in XML files) is used to map the image in the associated BMP File to the background MPM grid or the existing FEA mesh. In script scripted files, the command is

Origin (x0),(y0),<(z0)>,<(flip)>

In XML files, the command is:

<Origin x="(xO)" y="(yO)" z="(zO)" flipped="(flip)"/>

where

• (xO), (yO), and (zO) give the (x,y,z) coordinate for the origin of the image when mapped to the grid or mesh in length units (or determined by a units attribute in XML files). The (zO) coordinate is only needed for 3D calculations and is not allowed in FEA input files.
• If the optional (flip) is "yes", the origin will move to the upper-left corner of the image with y increasing in the downward direction and x increasing to the right. This change will flip the image in the y direction in the analysis compared to the image graphics. To provide (flip) parameter in scripted FEA files, you have to provide the (zO) parameter for proper argument alignment; it can be any number because it will be ignored.

If a BMPRegion block does not have an Origin command, the origin will be set to (0,0,0).

Intensity Command

The Intensity command within a BMPRegion block (or <BMP> element in XML files) has two uses to map wither materials or angles to the grid or elements.

Mapping Material Type

In this form, an Intensity command is used to map levels in the gray-scale of the associated BMP File to different types of material points or to different material initial conditions in an MPM analysis. For FEA calculations, it is used to map the image to different types of materials to assign to mesh elements. In scripted files, this use has the format:

Intensity (matID),(grayMin),(grayMax),<(prop),(value)>,…

In XML files, this use has the format:

<Intensity mat="(matID)" imin="(grayMin)" imax="(grayMax)">
    (property command options)
</Intensity>

where

• (matID) is the material ID for a previously defined material.
• (grayMin) to (grayMax) defines a range in gray-scale intensities to map to this material. The numbers must be from 0 (for black) to 255 (for white) and (grayMin) must be less than or equal to (grayMax).

In scripted files, the optional pairs of arguments, <(prop),(value)> are used to specify other initial conditions for the particles in the intensity range In each pair, the first parameter defines the property and the second parameter defines the value. The properties that are valid for both FEA and MPM input files are:

• "thick" for particle or element thickness in planar 2D calculations. The units are length units.
• "angle" for rotation angle of for the material about the z axis, which is only relevant for anisotropic materials. The units are degrees.
• "temp" for particle temperature. The units are degrees K.

The additional property options for MPM input files are:

• "vx" for particle x-direction velocity (R direction is axisymmetric). The units are velocity units.
• "vy" for particle y-direction velocity (Z direction is axisymmetric). The units are velocity units.
• "vz" for particle z-direction velocity in 3D MPM. The units are velocity units.
• "conc" for particle concentration (set as concentration potential from 0 to 1).

In XML files, all properties are set by commands that are subordinate to the <Intensity> element. The properties that are valid for both FEA and MPM input files are:

<Thickness>(value)</Thickness>
<Angle>(value)</Angle>
<Temperature>(value)</Temperature>

The additional property options for MPM input files are:

<vel x="(value)" y="(value)" z="(value)"/>
<Concentration>(value)</Concentration>

The units for each property (value) are the same as of script files (or determined by a units attribute).

Mapping Angles

When the first argument to the Intensity command is "angles" (or actually any text that is not a material ID), then that command is used to map gray-scale values in an associated angles mask BMP file to material angle for elements in an FEA mesh or material points in an MPM model. This use of the Intensity command only makes sense when optional (anglePath)s are used in the BMPRegion command. Angle mapping for more than one (anglePath) file in 3D simulations can be done by using more than one Intensity command. Each extra command maps the corresponding (anglePath) file in order provided. If there are fewer Intensity commands then (anglePath) files, the map from the last Intensity command will be used for remaining files

In scripted files, the angle mapping form of the command is:

Intensity "angles",(gray1),(gray2),(angle1),(angle2)

In XML files, this form of the command is:

<Intensity imin="(gray1)" imax="(gray2)" minAngle="(angle1)" maxAngle="(angle2)"/>

where ((gray1),(angle1)) and ((gray2),(angle3)) define two points. The angle will be calculated by a linear interpolation of gray scale to angle (in degrees) using the line that goes through these two points. The resulting angle, θ, for any given gray-scale value, g, will be:

      [math]\displaystyle{ \theta = (angle1) + {(angle2)-(angle1)\over (gray2)-(gray1)} \bigl(g-(gray1)\bigr) }[/math]

This interpolation applies to all gray scale values, including those outside the range (gray1) to (gray2)