Elastic Anisotropy - 3D Wave Surfaces

NPIB1.6 form submits a batch job to compute wave surfaces
of a fourth order stiffness tensor, Cijkl for
material with symmetry up to triclinic.
Stiffness entered for Calcium Formate with orthorhombic symmetry
Instructions for using this form:
    1. Enter appropriate numbers in the boxes,
    2. enter your email address,
    3. click on submit, and
    4. wait for results to be returned to your email. (this will take about 8 minutes)
    5. Be patient and NPIB1.6 will open up a new browser link to the working directory
      where you can watch the execution and file generation in real-time by refreshing.

  1. You can either select web links in the email or view the results directly by going to the directory
    http://www.jwave.vt.edu/output/kriz/cijkl/ "unique email-date-time"/. If your email does not provide direct web links, copy and paste the web address from the email into your web browser location window.
  2. All results are organized in one file:
    http://www.jwave.vt.edu/output/kriz/cijkl"unique email-date-time" /results.html
    If the form is submitted "as-is", here is an archived example: cijkl_results.html
  3. You should check the files dw2ds.out and dw2ds.err to verify that the job ran correctly.
  4. You can also download files from your web browser to your computer for archiving. If you are in the SMVC we will provide a 4.6Gbyte read/write optical disk for each student so that they can store their large simulation files. NOTE: ALL FILES WILL BE DELETED AFTER 3 DAYS.
  5. If you submit the form "as-is" you can view the VRML files (*.wrl), as shown below, with the cosmo vrml plugin. You can install the COSMO plugin on your web browser at no cost. A problem statement provides more detailed information on this particular solution. A more comprehensive development of the Christofel's equation is located in the ESM-MSE5984: (class-notes) section on Geometric Representations of Elastic Anisotropy: All Tensor Components, Cijkl

    Figure 1. Calcium Formate wave surfaces calculated from stiffnesses listed in Table 1.

    ---- Outermost --------- Intermediate ------- Innermost --------- Combined ----
    --- wavesurf1.wrl ------ wavesurf2.wrl ------ wavesurf3.wrl ------- glyph.wrl ----

Table 1. Representative orthorhombic symmetries.

Material ( Stiffnesses, GPa ) Density
gm/cm3		 C11 C22 C33 C44 C55 C66 C12 C13 C23
Benzene (orthorhomibic Type-1)
( C11, C22, C33 ) > ( C44, C55, C66 ) 		1.06 6.14 6.56 5.83 1.97 3.78 1.53 3.52 4.01 3.90
Calcium Formate (orthorhombic Type-2)
( C11> C33> C 66> C22> C55> C 44 ) 		2.02 49.2 24.4 35.4 10.5 12.2 28.2 24.8 24.5 14.5
Hypothetical (orthorhombic Type-3)
( C11> C66> C55> C22> C44> C33 ) 		6.00 180.0 45.2 10.3 20.4 45.5 90.6 0.100 0.200 0.300
Hypothetical (orthorhombic Type-4)
( C11> C22> C66> C44> C55> C33 ) 		3.00 80.1 60.2 10.3 30.4 20.5 40.6 0.100 0.200 0.300