3.3. Anisotropic Elasticity

Anisotropic elastic capability (TB,ANEL or TB,ELAS,,,,AELS/AELF) is available with current-technology plane and solid elements. Input the elastic coefficient matrix [D] either by specifying the stiffness constants (EX, EY, etc.) with MP commands, or by specifying the terms of the matrix via data-table commands (TB). The matrix should be symmetric and positive definite (requiring all determinants to be positive).

The full 6 x 6 elastic coefficient matrix [D] relates terms ordered x, y, z, xy, yz, xz via 21 constants as shown below.

For 2D problems, a 4 x 4 matrix relates terms ordered x, y, z, xy via 10 constants (D11, D21, D22, D31, D32, D33, D41, D42, D43, D44). The order of the vector is expected as {x, y, z, xy, yz, xz}, whereas for some published materials the order is given as {x, y, z, yz, xz, xy}. This difference requires the "D" matrix terms to be converted to the expected format. The "D" matrix can be defined in either "stiffness" form (with units of Force/Area operating on the strain vector) or in "compliance" form (with units of the inverse of Force/Area operating on the stress vector), whichever is more convenient. Both forms use the same data-table input.

Define the elastic coefficient matrix via the TB family of commands:

  1. Initialize the constant table (TB,ANEL or TB,ELAS,,,,AELS/AELF). Select the stiffness or flexibility form via the appropriate TBOPT value.

  2. Define the temperature (TBTEMP), or issue the TBFIELD command with TB,ELAS to input temperature or other supported field variables.

  3. Specify up to 21 constants (TBDATA).

Constant Meaning
C1-C6Terms D11, D21, D31, D41, D51, D61
C7-C12Terms D22, D32, D42, D52, D62, D33
C13-C18Terms D43, D53, D63, D44, D54, D64
C19-C21Terms D55, D65, D66

For TB,ANEL, you can define up to six temperature-dependent sets of constants (via NTEMP = 1 through 6). Matrix terms are linearly interpolated between temperature points.

Temperature dependence via NTEMP on the TB,ANEL command is not supported for coupled-field analyses.

In a piezoelectric analysis using coupled-field elements PLANE222, PLANE223, SOLID225, SOLID226, or SOLID227, you can define temperature-dependent elasticity coefficients via TB,ANEL (with TBOPT = 0) and tabular input on the TBDATA command:

TBDATA,STLOC,%tabname%

where tabname is the name of a table array parameter (*DIM) with TEMP as a primary variable. For more information, see Defining Linear Material Properties Using Tabular Input.

For a list of the elements that support this material model, see Material Model Support for Elements.