Helius PFA expresses constitutive relations and computes stress in the principal material coordinate system of the composite material. For unidirectional microstructures, the default principal material coordinate system is oriented with the '1' direction aligned with the fiber direction, while the '2' and '3' directions lie in the composite material's plane of transverse isotropy. However, in situations where it adds convenience or simplicity to the model creation process, you may change the orientation of the product's principal material coordinate system so that the '2' direction is aligned with the fiber direction, while the '1' and '3' directions lie in the composite material's plane of transverse isotropy.
For woven microstructures, the default principal material coordinate system is oriented with the '1' direction aligned with the fill tow direction, while the '2' direction corresponds to the warp tow direction and the '3' direction corresponds with the out-of-plane direction. However, in situations where it adds convenience or simplicity to the model creation process, you may change the orientation of the principal material coordinate system so that the '2' direction is aligned with the fill tow direction, while the '1' direction corresponds to the warp tow direction. Additionally, you may change the orientation of the principal material coordinate system so that the '3' direction is aligned with the fill tow direction while the '2' direction corresponds to the warp tow direction.
The 2nd user material constant is used to specify the orientation of the principal material coordinate system that will be used. The numerical value (1 or 2 for unidirectional materials and 1, 2 or 3 for woven materials) of the 2nd user material constant specifies which of the principal material coordinate axes will be aligned with the fiber direction (for unidirectional composites) or the fill tow direction (for woven composites). The availability of alternative orientations for the principal material coordinate system provides you with more flexibility in specifying the orientation of the material plies within a section definition.
You should be aware that Abaqus/Standard outputs the composite average state of stress and strain in the coordinate system that is specified by the second user material constant; however, the constituent average states of stress and strain (stored in SDV7, SDV8, ..., SDV90) are always output in Helius PFA's default principal material coordinate system. As an example, if the second user material constant is specified as 2, all composite average stress and strain states will be output in the local system you define, with the local 2 direction corresponding to either the longitudinal axis of the fibers for unidirectional materials, or the fill axis for woven materials. However, all constituent average stress and strain states will be reported in the default principal coordinate system of the unidirectional or woven composite material.
- For unidirectional microstructures, the default principal material coordinate system is oriented with the '1' direction aligned with the fiber direction, while the '2' and '3' directions lie in the composite material's plane of transverse isotropy.
- For woven microstructures, the default principal material coordinate system is oriented with the '1' direction aligned with the fill tow direction, while the '2' direction corresponds to the warp tow direction and the '3' direction corresponds with the out-of-plane direction.
Consider the following *USER MATERIAL statement that appears in an Abaqus input file representing a unidirectional microstructure.
*USER MATERIAL, CONSTANTS=16 1, 2, 1, 0, 0, 0, 0, 0 0, 0, 0, 0.1, 0.01, 0, 0, 0
Note that the second user material constant is assigned a value of 2. Therefore, this particular material will use a principal material coordinate system where the '2' axis is aligned with the reinforcing fibers, and the '1' and '3' axes lie in the composite material's plane of transverse isotropy. The following example problem illustrates the consequences of assigning the second user material constant a value of 2.
Example
Consider a cylindrical tube composed of two unidirectional composite material plies. Both composite plies are made of the same composite material, but the two plies differ in the orientation of the reinforcing fibers. The reinforcing fibers of the inner ply are aligned with the axial direction of the cylinder, and the reinforcing fibers of the outer ply are aligned with the hoop direction of the cylinder. The red lines in the image below show the orientation of the reinforcing fibers in the inner and outer composite plies.
To illustrate the consequences of specifying a value of 2 for the second user material constant, consider the following statements that are excerpted from an Abaqus input file. The second user material constant is assigned a value of 2 indicating that the '2' axis of the principal material coordinate system is aligned with the reinforcing fibers. Note that ** indicates a comment in an Abaqus input file.
** Define a Helius PFA composite material.
** Note that the ‘2’ axis of the principal material
** coordinate system is aligned with the fiber direction.
*MATERIAL, name=IM7_8552
*DEPVAR
7
*USER MATERIAL, CONSTANTS=16
1, 2, 1, 0, 0, 0, 0, 0
0, 0, 0, 0.1, 0.01, 0, 0, 0
**
** Define a local cylindrical coordinate system for the
** inner composite ply. Note that the local cylindrical
** coordinate system is rotated so that the local ‘2’ axis
** points in the global axial direction.
*Orientation, name=axial_fibers, system=CYLINDRICAL
0., 0., 0., 0., 0., 1.
1, 90.
**
** Define a solid section for the inner composite ply.
*Solid Section, elset=innerPly, orientation=axial_fibers, material=IM7_8552
**
** Define a local cylindrical coordinate system for the
** outer composite ply. Note that there is no need to
** rotate the local cylindrical coordinate system since
** the local ‘2’ axis points in the global hoop direction.
*Orientation, name=hoop_fibers, system=CYLINDRICAL
0., 0., 0., 0., 0., 1.
1, 0.
**
** Define a solid section for the outer composite ply.
*Solid Section, elset=outerPly, orientation=hoop_fibers, material=IM7_8552
Notice that the orientation of the local cylindrical coordinate systems (given in the *ORIENTATION statements) must be consistent with the convention chosen for the principal material coordinate system. For example, the local cylindrical coordinate system for the inner ply is rotated so that the local '2' axis always points in the global axial direction. In contrast, the local cylindrical coordinate system for the outer ply does not need to be rotated since its local '2' axis always points in the global hoop direction.