Trelis 16.3 User Documentation
The metrics used for hexahedral elements in Trelis are summarized in the following table:
Function Name

Dimension

Full Range

Acceptable Range

Reference

Aspect Ratio

L^0

1 to inf

1 to 4

1

Skew

L^0

0 to 1

0 to 0.5

1

Taper

L^0

0 to +inf

0 to 0.4

1

Element Volume

L^3

inf to inf

None

1

Stretch

L^0

0 to 1

0.25 to 1

2

Diagonal Ratio

L^0

0 to 1

0.65 to 1

3

Dimension

L^1

0 to inf

None

1

Condition No.

L^0

1 to inf

1 to 8

5

Jacobian

L^3

inf to inf

None

5

Scaled Jacobian

L^0

1 to +1

0.5 to 1

5

Shear

L^0

0 to 1

0.3 to 1

5

Shape

L^0

0 to 1

0.3 to 1

5

Relative Size

L^0

0 to 1

0.5 to 1

5

Shear & Size

L^0

0 to 1

0.2 to 1

5

Shape & Size

L^0

0 to 1

0.2 to 1

5

Distortion

L^0

0 to 1

0.6 to 1

6

Unless otherwise noted, Trelis supports calculations for linear hexahedral elements. Metric calculations involving higherorder hexahedral elements will only use the corner nodes of the element.
Aspect Ratio: Maximum edge length ratios at hex center.
Skew: Maximum cos A where A is the angle between edges at hex center.
Taper: Maximum ratio of lengths derived from opposite edges.
Element Volume: Jacobian at hex center.
Stretch: Sqrt(3) * minimum edge length / maximum diagonal length.
Diagonal Ratio: Minimum diagonal length / maximum diagonal length.
Dimension: Prontospecific characteristic length for stable time step calculation. Char_length = Volume / 2 grad Volume.
Condition No. Maximum condition number of the Jacobian matrix at 8 corners.
Jacobian: Minimum pointwise volume of local map at 8 corners & center of hex.
Scaled Jacobian: Minimum Jacobian divided by the lengths of the 3 edge vectors.
Shear: 3/Mean Ratio of Jacobian Skew Matrix
Shape: 3/Mean Ratio of weighted Jacobian Matrix
Relative Size: Min(J, 1/J), where J is the determinant of weighted Jacobian matrix
Shear & Size: Product of Shear and Size Metrics
Shape & Size: Product of Shape and Size Metrics
Distortion: {min(J)/actual volume}*parent volume, parent volume = 8 for hex