Shear Matrix Strain

Group: Lattice | Class: ShearMatrixCard

What the card does

Generate off-diagonal deformations by scanning xy, yz, and xz shear-matrix components, each with an independent minimum, maximum, and step.

\[\begin{split}\gamma_{xy}=\frac{s_{xy}}{100},\quad \mathbf{S}=\begin{bmatrix}1&\gamma_{xy}&\gamma_{xz}\\0&1&\gamma_{yz}\\0&0&1\end{bmatrix},\quad \mathbf{C}'=\mathbf{C}\mathbf{S}\end{split}\]

With symmetric=true, matching lower-triangular entries are filled to form a symmetric strain-like path.

Example workflow

Scenario: Predicted C44 is 40% below DFT

An fcc Al NEP reproduces C11 and C12 but predicts only 60% of the DFT C44. Its training set contains axial strains but no off-diagonal shear states.

Diagnosis: Shear elastic constants derive from off-diagonal strain response. Add cells with controlled shear components so that response is interpolated.

Input: A relaxed fcc Al cell.

Objective: Scan symmetric xy shear from -3% to +3% in 1% steps.

Parameters:

xy_range = [-3, 3, 1]
yz_range = [0,0,1] (one zero point; the step must be nonzero)
xz_range = [0,0,1]
symmetric = true

Output: Seven structures with xy from -0.03 to +0.03 and zero yz/xz components.

How to verify that training-set quality improved:

After labeling and retraining, recompute the elastic tensor; C44 should approach the DFT reference.
Inspect resulting cell angles and confirm that nonorthogonality remains in the intended range.
If C44 improves but C55/C66 do not, scan yz and xz separately.
Open all three ranges only when joint coverage is needed; output is Nxy × Nyz × Nxz.

When to add this card

Add it when:

Shear modulus or off-diagonal elastic response is systematically wrong
Training lacks nonorthogonal cells
Stress-strain response along shear directions is needed

Do not add it when:

Only volume and axial strain are needed; use Lattice Strain
Shear should be controlled through crystallographic angles; use Shear Angle Strain
The system is molecular and shear would distort intramolecular topology without molecular protection

Parameters

XY Range（xy_range）

tuple[float, float, float], default (-5.0,5.0,1.0). xy scan as [min,max,step] in percent; 5 means matrix component 0.05. Use [0,0,1] for an inactive channel.

YZ Range（yz_range）

tuple[float,float,float], default (-5.0,5.0,1.0). yz scan with the same syntax; use [0,0,1] when inactive.

XZ Range（xz_range）

tuple[float,float,float], default (-5.0,5.0,1.0). xz scan with the same syntax; use [0,0,1] when inactive.

Output is Nxy × Nyz × Nxz. Three default 11-point channels produce 1,331 structures. Validate one channel first.

Symmetric（symmetric）

bool, default true. Mirror upper-triangular components into the lower triangle, for example S[1,0]=S[0,1]. Disable only for an intentionally asymmetric deformation path.

Identify Organic（identify_organic）

bool, default false. Enable molecular protection for molecular crystals; leave disabled for purely inorganic systems.

Recommended presets

Single-component elastic sampling (xy only, ±3%, symmetric)

{
  "class": "ShearMatrixCard",
  "check_state": true,
  "xy_range": [-3, 3, 1],
  "yz_range": [0, 0, 1],
  "xz_range": [0, 0, 1],
  "symmetric": true,
  "identify_organic": false
}

Two-component shear coverage (xy and yz, ±5%, symmetric, about 121 outputs)

{
  "class": "ShearMatrixCard",
  "check_state": true,
  "xy_range": [-5, 5, 1],
  "yz_range": [-5, 5, 1],
  "xz_range": [0, 0, 1],
  "symmetric": true,
  "identify_organic": false
}

Three-channel study (±6%, step 2%, asymmetric, about 343 outputs)

{
  "class": "ShearMatrixCard",
  "check_state": true,
  "xy_range": [-6, 6, 2],
  "yz_range": [-6, 6, 2],
  "xz_range": [-6, 6, 2],
  "symmetric": false,
  "identify_organic": false
}

Recommended combinations

Lattice Strain -> Shear Matrix Strain: cover axial response before shear tensor components
Shear Matrix Strain -> Atomic Perturb: add coordinate noise after a shear deformation
Super Cell -> Shear Matrix Strain: shear at the intended cell scale

Common questions

No output. Every step must be positive; use [0,0,1] for an inactive component.

Output explodes. Three channels form a Cartesian product. Validate one channel and estimate the total before adding more.

Geometry becomes implausible. Excessive shear can make the lattice ill-conditioned. Inspect nearest-neighbor distances and the cell determinant, increasing beyond ±5% gradually.

Matrix or angle shear? Matrix shear directly controls Cartesian off-diagonal components and aligns with elastic-tensor calculations. Angle shear controls alpha, beta, and gamma and aligns with crystallographic descriptions. They are distinct paths and may be complementary.

Output labels

Shr(xy={sxy}%,yz={syz}%,xz={sxz}%,sym={0|1})

Reproducibility

Deterministic: all components are scanned on a fixed grid.