Parameters file

The parameters.toml file configures simulations in fragma. This section gives a broad (and non-exhaustive) overview of its organization. It is organized into sections, each defining a specific aspect of the simulation. For practical examples, refer to examples.

`[model]`

name: Type of simulation ("elasticity", "fracture").
dim: Dimensionality of the problem (2) , 3 works only with elasticity.
2D_assumption (if 2D): Assumption for 2D problems ("plane_strain", "plane_stress").
model (if fracture): Phase-field model type (e.g., "AT1", "AT2").

`[mesh]`

msh_file: Name of the mesh file (e.g., "mesh.msh").
[mesh.physical_groups]: Physical groups defined in the mesh, used for boundary conditions or material properties.
```
[mesh.physical_groups]
left  = 5
right = 6
```
Physical groups can also be set as crack (α=1) or non-crackable (α=0).
```
[mesh.physical_groups]
non-crackable_1 = 9
non-crackable_2 = 10
crack = 4
```

`[mechanical]`

Material properties:
E: Young’s modulus (in Pa).
nu: Poisson’s ratio.
Gc (if fracture): Critical energy release rate (in J/m²).
ell (if fracture): Regularization length (in m).

`[loading]`

Boundary conditions:
- [loading.u_imp_max]: Imposed displacements.
```
[loading.u_imp_max]
left  = [0, 0]
```
- [loading.f_imp_max]: Imposed forces.
```
[loading.f_imp_max]
right = [0.1, nan]
```
Path-following:
```
[loading]
constraint = "max_inc_undamaged_elastic_energy"
dtau = 2e5
```
The constraint corresponds to the name of the constraint equation and dtau to the step size. The available constraint are : "max_strain_inc_outside_crack" (recommended), "load_factor_inc" (no path-following), "max_strain_inc", "nodal_disp_inc", "local_arc_length", "crack_driving_variable", and "maxt_crack_driving_variable".

Note

nan in the imposed displacement vector means that no displacement is imposed.

`[numerical]`

Solver parameters:
utol: Displacement tolerance.
atol (if fracture): Phase-field tolerance.
max_iter (if fracture): Maximum number of iterations in alternate minimization.
alpha_res (if fracture): Residual tolerance for non-linear solution of the phase-field.
omega (optional): Over-relaxation parameter.

`[end]`

Termination criterion:
criterion: "t" (time-based), "elastic_energy_drop".
t_max: Maximum simulation step.
drop: Drop in elastic energy (E(t) / max_{t’≤t} E(t’) < drop).

`[postprocess]` (optional)

Post-processing options:
[postprocess.probes]: Coordinates for displacement probes.

[postprocess.probes] displacement = [ [0, 0.5, 0], [10, 0.5, 0], ]

Example File

[model]
name = "fracture"
dim = 2
2D_assumption = "plane_stress"
model = "AT1"

[mesh]
msh_file = "mesh.msh"

[mesh.physical_groups]
bot = 37
top = 38
crack = 39

[mechanical]
E = 3e9
nu = 0.4
Gc = 380
ell = 0.1

[numerical]
utol = 1e-6
atol = 1e-5
max_iter = 1000
alpha_res = 1e-12

[loading]
[loading.u_imp_max]
bot = [0, -5e-4]
top = [0,  5e-4]

[end]
criterion = "t"
t_max = 50

Key Notes

Physical Groups: Must match those defined in the mesh file.
Optional Sections: Some sections (e.g., [numerical], [postprocess]) are optional.

Parameters file

[model]

[mesh]

[mechanical]

[loading]

[numerical]

[end]

[postprocess] (optional)