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

Dimension

Full Range

Acceptable Range

Reference

Aspect Ratio Beta

L^0

1 to inf

1 to 3

1

Aspect Ratio Gamma

L^0

1 to inf

1 to 3

1

Element Volume

L^3

inf to inf

None

1

Condition No 
L^0

1 to inf

1 to 3

2

Jacobian

L^3

inf to inf

None

2

Scaled Jacobian

L^0

1 to 1

0.2 to 1

2

Shape

L^0

0 to 1

0.2 to 1

3

Relative Size

L^0

0 to 1

0.2 to 1

3 
Shape and Size 
L^0

0 to 1

0.2 to 1

3

Distortion 
L^0

1 to 1

0.6 to 1

4

Equivolume Skew  Fluent  
Tet Squish  Fluent 
Unless otherwise noted, Trelis supports calculations for linear tetrahedral elements. Metric calculations involving higher order tetrahedral elements will only use the corner nodes of the element.
Aspect Ratio Beta: CR / (3.0 * IR) where CR = circumsphere radius, IR = inscribed sphere radius
Aspect Ratio Gamma: Srms**3 / (8.479670*V) where Srms = sqrt(Sum(Si**2)/6), Si = edge length
Element Volume: (1/6) * Jacobian at corner node
Condition No.: Condition number of the Jacobian matrix at any corner
Jacobian: Minimum pointwise volume at any corner
Scaled Jacobian: Minimum Jacobian divided by the lengths of 3 edge vectors
Shape: 3/Mean Ratio of weighted Jacobian Matrix
Relative Size: Min(J, 1/J), where J is the determinant of the weighted Jacobian matrix
Shape & Size: Product of Shape and Relative Size Metrics
Distortion: {min(J)/actual volume}*parent volume, parent volume = 1/6 for tet
Equivolume Skew: (metric used by Fluent)
Tet Squish: (metric used by Fluent)
For tetra10 elements, the distortion metric can be used in conjunction with the shape metric to determine whether the midedge nodes have caused negative Jacobians in the element. The shape metric only considers the linear (parent) element. If a tetra10 has a nonpositive shape value then the element has areas of negative Jacobians. However, for elements with a positive shape metric value, if the distortion value is nonpositive then the element contains negative Jacobians due to the midside node positions.
Note that, for tetrahedral elements, there are several definitions of the term "aspect ratio" used in literature and in software packages. Please be aware that the various definitions will not necessarily give the same or even comparable results.