The Schmidt factor is a key parameter in crystallographic slip theory; it represents the resolved shear stress for a particular slip system. It is calculated as the dot product of the stress vector acting on a crystal and the slip direction projected onto the slip plane. Its value ranges from 0 to 0.5.

In the DAMASK (the Düsseldorf Advanced Material Simulation Kit) material simulation software, you can calculate the Schmidt factors using the Schmid() function in the Orientation class. Here's how you might do it:

This is a general overview of the process. The actual implementation would depend on your simulation's specifics and crystal system. Please consult the DAMASK documentation and user community for further assistance, as they may provide specific scripting or functionality for calculating Schmidt factors.

Joshua Depiver Is there a ready-made formula for the final step for me to understand: assuming that the 3 x 3 stress matrix is A and the 3 x 3 Schmidt matrix of the （111）[01-1] slip system is B, how can I calculate the Schmidt factor?

I don't quite understand the specific calculation method in Part Four.

The Schmid factor, named after the metallurgist Ernst Schmid, is a scalar quantity that indicates the resolved shear stress for a given slip system. It is used in materials science to predict the likelihood of slip on a particular crystallographic plane and direction.

The Schmid factor (m) can be calculated as:

m = cos(λ) * cos(ϕ)

where:

• λ is the angle between the applied stress direction and the slip direction (in the slip plane), and
• ϕ is the angle between the normal to the slip plane and the applied stress direction.

You are asked to calculate the Schmid factor using stress matrix 'A' and Schmidt matrix of the (111)[01-1] slip system 'B'.

In a cubic crystal system such as FCC, the (111) plane and the [01-1] direction is a common slip systems. In this case, the direction cosines (which relate to the angles λ and ϕ) can be calculated from the normal to the plane (for the (111) plane in this case) and the direction vector (the [01-1] direction in this case).

However, the direct calculation of the Schmid factor using stress matrix 'A' and Schmid matrix 'B' is unusual, as the Schmid factor is usually calculated geometrically. If you have the stress matrix and the transformation matrix for the slip system (which I suspect you mean by 'Schmid matrix'), you might be asked to calculate the resolved shear stress (not the Schmid factor). The resolved shear stress (τ) is calculated as:

τ = σ * m

where σ is the applied stress. In matrix form, this could be computed as:

τ = m' * A * m

where A is the stress matrix, and m is the Schmid factor represented in a direction cosine matrix form (a transformation matrix for the slip system).

Please refer to your course notes, textbook, or instructor for more specific information on how to proceed, as the method might be specific to the course or context.

Ming Guo, if we assume that the (Cauchy) stress tensor in the laboratory frame is termed A with shape (3,3) and a bunch of orientations (with corresponding `lattice` properly specified, e.g. "cI") are stored as the damask.Orientation object O, then the Schmid factors for each slip system of each orientation under the acting stress A can be found as

```

SF = np.einsum('...ij,ij', O.Schmid(N_slip=[12,12]), A)

```

The "[12,12]" specifies to use all 12 {110} and 12 {112} slip systems of the bcc lattice that we exemplarily assumed here. For 'cF', you would use "[12]", since there is only one slip family (i.e. {111}) with a total of 12 slip systems.