Simulation Output¶

In this section the output files are described. In general, the output can be broken down into four types: nodal output (variables that are calculated and printed at the finite element nodes), elemental output (variables that are calculated and printed at the finite elements), restart output (which contains all variables necessary to restart a simulation at a specific load step), and miscellaneous output (macroscopic forces and various simulation statistics).

All desired output must be defined in the simulation.config file (see: Printing Results for a description of the print options). A (small) post.report file is systematically printed, which contains information necessary for post-processing with Neper. All output described in this section is raw simulation output and can be post-processed into a more human-readable format with Neper’s -S module. Refer to the Neper reference manual, for a more complete description of the -S module.

Nodal Output¶

Nodal output prints a single variable per finite element node. Raw output is printed on a per-core basis, and the general file name structure is post.variable.core<#>, where variable is the variable being printed, and <#> denotes the ID of the core on which the data is being printed. In general, the file structure is:

<step_number> <core_start_dof> <core_end_dof>
<node_N> <values>
<node_N+1> <values>
<node_N+2> <values>
...
<step_number> <core_start_dof> <core_end_dof>
<node_N> <values>
<node_N+1> <values>
<node_N+2> <values>
...

Here, a header line prints for each deformation step, which details the deformation step number (<step_number>), the initial degree of freedom that prints from that core (<core_start_dof>), and the final degree of freedom that prints from that core (<core_end_dof>). Note that the number of nodes per-core is one third of the number of degrees of freedoms per-core. For each load step, multiple values associated with a variable are printed per line (<values>), preceded by the corresponding node number (<node_*>). When multiple values are printed per line, values are space delimited.

Below, the specific nodal values available for printing are explained in detail.

Coordinates¶

In the post.coo.core* files, the coordinates are printed. Each nodal coordinate is described in the orthonormal Cartesian sample basis, and one coordinate is printed per line (3 values per line). The components of the coordinates are printed in the order:

\(x, y, z\)

Displacements¶

In the post.disp.core* files, the displacements are printed. Each nodal displacement is described in the orthonormal Cartesian sample basis, and one displacement is printed per line (3 values per line). The components of the displacements are printed in the order:

\(d_x, d_y, d_z\)

Velocities¶

In the post.vel.core* files, the velocities are printed. Each nodal velocity is described in the orthonormal Cartesian sample basis, and one velocity is printed per line (3 values per line). The components of the velocities are printed in the order:

\(v_x, v_y, v_z\)

Elemental Output¶

Elemental output prints a single variable per finite element. Raw output is printed on a per-core basis, and the general file name structure is post.variable.core<#>, where variable is the variable being printed, and <#> denotes the ID of the core on which the data is being printed. In general, the file structure is:

<step_number> <core_start_elt> <core_end_elt>
<element_N> <value(s)>
<element_N+1> <value(s)>
<element_N+2> <value(s)>
...
<step_number> <core_start_elt> <core_end_elt>
<element_N> <value(s)>
<element_N+1> <value(s)>
<element_N+2> <value(s)>
...

Here, a header line prints for each deformation step, which details the deformation step number (<step_number>), the initial element that prints from that core (<core_start_elt>), and the final element that prints from that core (<core_end_elt>). For each load step, either a single or multiple value (<value(s)>) associated with a variable is printed per line (for variables that are printed singularly per element, such as scalars, or for variables that print multiple values per element, such as tensors, respectively), preceded by the corresponding element number (<element_*>). When multiple values are printed per line, values are space delimited.

FEPX calculates elemental quantities at each Gauss quadrature point within the element (15 total). However, only one value is printed – that associated with the quadrature point that falls at the element centroid.

Below, the specific nodal values available for printing are explained in detail.

Critical Resolved Shear Stress¶

In the post.crss.core* files, the critical resolved shear stress is printed. For the isotropic hardening assumption (Optional Input Parameters), one value is printed per element. For anisotropic hardening assumptions, the critical resolved shear stress is printed for each slip system per element, one line of values per element.

For body centered cubic crystal symmetry, values are printed in the order:

\((0 1 \bar 1)[1 1 1],\,(1 0 \bar 1)[1 1 1],\,(1 \bar 1 0)[1 1 1],\,(0 1 1)[1 1 \bar 1],\,(1 0 1)[1 1 \bar 1],\,(1 \bar 1 0)[1 1 \bar 1],\)

\((0 1 1)[1 \bar 1 1],\,(1 0 \bar 1)[1 \bar 1 1],\,(1 1 0)[1 \bar 1 1],\,(0 1 \bar 1)[1 \bar 1 \bar 1],\,(1 0 1)[1 \bar 1 \bar 1],\,(1 1 0)[1 \bar 1 \bar 1]\).

For face centered cubic crystal symmetry, values are printed in the order:

\((1 1 1)[0 1 \bar 1],\,(1 1 1)[1 0 \bar 1],\,(1 1 1)[1 \bar 1 0],\,(1 1 \bar 1)[0 1 1],\,(1 1 \bar 1)[1 0 1],\,(1 1 \bar 1)[1 \bar 1 0],\,\)

\((1 \bar 1 1)[0 1 1],\,(1 \bar 1 1)[1 0 \bar 1],\,(1 \bar 1 1)[1 1 0],\,(1 \bar 1 \bar 1)[0 1 \bar 1],\,(1 \bar 1 \bar 1)[1 0 1],\,(1 \bar 1 \bar 1)[1 1 0]\).

For hexagonal close packed crystal symmetry, values are printed in the order (corresponding to the 3 basal, 3 prismatic, and 12 pyramidal slip systems):

\((0 0 0 1)[2 \bar 1 \bar 1 0],\,(0 0 0 1)[\bar 1 2 \bar 1 0],\,(0 0 0 1)[\bar 1 \bar 1 2 0],\,(0 1 \bar 1 0)[2 \bar 1 \bar 1 0],\,(\bar 1 0 1 0)[\bar 1 2 \bar 1 0],\,(1 \bar 1 0 0)[\bar 1 \bar 1 2 0],\,\)

\((1 0 \bar 1 1)[\bar 2 1 1 3],\,(1 0 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[2 \bar 1 \bar 1 3],\,\)

\((\bar 1 0 1 1)[2 \bar 1 \bar 1 3],\,(\bar 1 0 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 2 1 1 3]\).

For body centered tetragonal crystal symmetry, values are printed in the order:

\((1 0 0)[0 0 1],\,(0 1 0)[0 0 1],\,(1 1 0)[0 0 1],\,(1 \bar 1 0)[0 0 1],\,(1 0 0)[0 1 0],\,(0 1 0)[1 0 0],\)

\((1 1 0)[1 \bar 1 1],\,(1 1 0)[\bar 1 1 1],\,(1 \bar 1 0)[1 1 1],\,(1 \bar 1 0)[\bar 1 \bar 1 1],\,(1 1 0)[\bar 1 1 0],\,(1 \bar 1 0)[1 1 0],\)

\((1 0 0)[0 1 1],\,(1 0 0)[0 1 \bar 1],\,(0 1 0)[1 0 1],\,(0 1 0)[1 0 \bar 1],\,(0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],\)

\((0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],\,(1 0 1)[1 0 \bar 1],\,(1 0 \bar 1)[1 0 1],\,(0 1 1)[0 1 \bar 1],\,(0 1 \bar 1)[0 1 1],\)

\((1 2 1)[\bar 1 0 1],\,(\bar 1 2 1)[1 0 1],\,(\bar 1 \bar 2 1)[1 0 1],\,(1 \bar 2 1)[\bar 1 0 1],\,(2 1 1)[0 \bar 1 1],\,(\bar 2 1 1)[0 \bar 1 1],\)

\((\bar 2 \bar 1 1)[0 1 1],\,(2 \bar 1 1)[0 1 1].\)

Deformation Rate Tensor¶

In the post.defrate.core* files, the deformation rate tensor is printed. Each tensor, \(\bf D\), is printed in the sample basis. The independent components are printed, one tensor per line (6 values per line). The components, \(D _{ij}\), are printed in the order:

\(D_{11},\,D_{22},\,D_{33},\,D_{23},\,D_{13},\,D_{12}\)

Equivalent Deformation Rate¶

In the post.defrate-eq.core* files, the equivalent deformation rate is printed. One scalar value is printed per element. The equivalent deformation rate, \(D\), is calculated based on the deformation rate tensor, \({\bf D}\), via the tensor inner product:

\(D = \sqrt{ {2 \over 3} {\bf D} : {\bf D} }\)

Plastic Deformation Rate Tensor¶

In the post.defrate-pl.core* files, the deviatoric plastic deformation rate tensor is printed. Each tensor, \({\bf D}^p\), is printed in the sample basis. The independent components are printed, one tensor per line (6 values per line). The components, \(D^p_{ij}\), are printed in the order:

\(D^p_{11},\,D^p_{22},\,D^p_{33},\,D^p_{23},\,D^p_{13},\,D^p_{12}\)

Equivalent Plastic Deformation Rate¶

In the post.defrate-pl-eq.core* files, the equivalent plastic deformation rate is printed. One scalar value is printed per element. The equivalent plastic deformation rate, \(D^p\), is calculated based on the plastic deformation rate tensor, \({\bf D}^p\), via the tensor inner product:

\(D^p = \sqrt{ {2 \over 3} {\bf D}^p : {\bf D}^p }\)

Elemental Volume¶

In the post.elt-vol.core* files, the elemental volume is printed. One scalar value is printed per element. The elemental volume is calculated as the Gaussian integration of the determinant of the Jacobian matrix:

\(V_{el} = \sum_{i=1}^{n_{qp}}{det(J_i) w_i }\)

Crystallographic Orientation¶

In the post.ori.core* files, the crystallographic orientation is printed. Depending on the orientation parameterization used as input, the orientation values may range from 3 values per element (when using Rodrigues vector, Euler-Bunge angles and Euler-Kocks angles parameterizations) or 4 values per element (when using axis-angle or quaternion parameterizations). One orientation is printed per line (3 or 4 values per line).

For Rodrigues: \(r_1,\,r_2,\,r_3\), where the Rodrigues vector is \({\bf r} = {\bf t} \tan{(\omega / 2)}\).

For Euler-Bunge: \(\phi_1,\,\theta,\,\phi_2\) (where \(\phi_1\) is the rotation about the \(z\) axis, \(\theta\) is the rotation about the \(x^{\prime}\) axis, and \(\phi_2\) is the rotation about the \(z^{\prime \prime}\) axis, all in degrees).

For Euler-Kocks: \(\Psi,\,\Theta,\,\phi\) (where \(\Psi\) is the rotation about the \(z\) axis, \(\Theta\) is the rotation about the \(y^{\prime}\) axis, and \(\phi\) is the rotation about the \(z^{\prime \prime}\) axis, all in degrees).

For axis-angle: \(t_1,\,t_2,\,t_3,\,\omega\) (where \(\bf{t}\) is the normalized axis of rotation and \(\omega\) is the angle of rotation about said axis, in degrees).

For quaternion: \(q_0,\,q_1,\,q_2,\,q_3\), where \(q_0 = \cos{(\omega / 2)}\) and \(q_i = t_i \sin{(\omega / 2)}\) for \(i = 1,\,2,\,3\).

Slip System Shear¶

In the post.slip.core* files, the accumulated slip system shear is printed. The slip system shear is printed for each slip system per element, one line of values per element.

For body centered cubic crystal symmetry, values are printed in the order:

\((0 1 \bar 1)[1 1 1],\,(1 0 \bar 1)[1 1 1],\,(1 \bar 1 0)[1 1 1],\,(0 1 1)[1 1 \bar 1],\,(1 0 1)[1 1 \bar 1],\,(1 \bar 1 0)[1 1 \bar 1],\) \((0 1 1)[1 \bar 1 1],\,(1 0 \bar 1)[1 \bar 1 1],\,(1 1 0)[1 \bar 1 1],\,(0 1 \bar 1)[1 \bar 1 \bar 1],\,(1 0 1)[1 \bar 1 \bar 1],\,(1 1 0)[1 \bar 1 \bar 1]\).

For face centered cubic crystal symmetry, values are printed in the order:

\((1 1 1)[0 1 \bar 1],\,(1 1 1)[1 0 \bar 1],\,(1 1 1)[1 \bar 1 0],\,(1 1 \bar 1)[0 1 1],\,(1 1 \bar 1)[1 0 1],\,(1 1 \bar 1)[1 \bar 1 0],\,\) \((1 \bar 1 1)[0 1 1],\,(1 \bar 1 1)[1 0 \bar 1],\,(1 \bar 1 1)[1 1 0],\,(1 \bar 1 \bar 1)[0 1 \bar 1],\,(1 \bar 1 \bar 1)[1 0 1],\,(1 \bar 1 \bar 1)[1 1 0]\).

For hexagonal close packed crystal symmetry, values are printed in the order (corresponding to the 3 basal, 3 prismatic, and 12 pyramidal slip systems):

\((0 0 0 1)[2 \bar 1 \bar 1 0],\,(0 0 0 1)[\bar 1 2 \bar 1 0],\,(0 0 0 1)[\bar 1 \bar 1 2 0],\,(0 1 \bar 1 0)[2 \bar 1 \bar 1 0],\,(\bar 1 0 1 0)[\bar 1 2 \bar 1 0],\,(1 \bar 1 0 0)[\bar 1 \bar 1 2 0],\,\) \((1 0 \bar 1 1)[\bar 2 1 1 3],\,(1 0 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[2 \bar 1 \bar 1 3],\,\) \((\bar 1 0 1 1)[2 \bar 1 \bar 1 3],\,(\bar 1 0 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 2 1 1 3]\).

For body centered tetragonal crystal symmetry, values are printed in the order:

\((1 0 0)[0 0 1],\,(0 1 0)[0 0 1],\,(1 1 0)[0 0 1],\,(1 \bar 1 0)[0 0 1],\,(1 0 0)[0 1 0],\,(0 1 0)[1 0 0],\) \((1 1 0)[1 \bar 1 1],\,(1 1 0)[\bar 1 1 1],\,(1 \bar 1 0)[1 1 1],\,(1 \bar 1 0)[\bar 1 \bar 1 1],\,(1 1 0)[\bar 1 1 0],\,(1 \bar 1 0)[1 1 0],\) \((1 0 0)[0 1 1],\,(1 0 0)[0 1 \bar 1],\,(0 1 0)[1 0 1],\,(0 1 0)[1 0 \bar 1],\,(0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],\) \((0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],\,(1 0 1)[1 0 \bar 1],\,(1 0 \bar 1)[1 0 1],\,(0 1 1)[0 1 \bar 1],\,(0 1 \bar 1)[0 1 1],\) \((1 2 1)[\bar 1 0 1],\,(\bar 1 2 1)[1 0 1],\,(\bar 1 \bar 2 1)[1 0 1],\,(1 \bar 2 1)[\bar 1 0 1],\,(2 1 1)[0 \bar 1 1],\,(\bar 2 1 1)[0 \bar 1 1],\) \((\bar 2 \bar 1 1)[0 1 1],\,(2 \bar 1 1)[0 1 1].\)

Slip System Shear Rate¶

In the post.sliprate.core* files, the slip system shear rate is printed. The slip system shear rate is printed for each slip system per element, one line of values per element.