How do we set the initial condition as a function of spatial coordinates

[ruanqc]

Hi, everyone,
I met a problem when using damask for setting the initial dislocation as a function of spatial coordinates. The problem detials are as follow,

if we want to set initial dislocation density as a function of x as, $\rho^\alpha_{e \pm}|_{t=0}= \rho_0 + N(x)$, where N(x) is the normal distribution, say that mean $\mu$ = L/2 at the center of domain length L, and standard derivation $\sigma^2$ = 1, illustrated as the red curve shape bellow. Then, how could we implement this initial condition in damask nonlocal plastic model (single crystal level)? Could we handle these initial condition in input files, such as geometry.vti or material.yaml? otherwise, are there any approaches to implement this initial condition

Thank you in advance, ruanqc

---

##illustration of initial disolcation densities

---

##material.yaml
N_sl: [1]
rho_u_ed_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_ed_pos_0: [1.25e9]
rho_u_sc_neg_0: [0.0]
rho_u_sc_pos_0: [0.0]
rho_d_ed_0: [0]
rho_d_sc_0: [0]

---

##geom.vti
import damask
import numpy as np
#GeomGrid
size = np.array([128, 128, 2])*1e-6 #Lx Ly Lz (unit in um)
cells = [128,128,2] # Nx Ny Nx
N_grains = 1
seeds = damask.seeds.from_random(size,N_grains,cells)
grid = damask.GeomGrid.from_Voronoi_tessellation(cells,size,seeds)
grid.save(f'geom_N{N_grains}_{cells[0]}x{cells[1]}x{cells[2]}') # output vti geom

[ruanqc]

In nonlocal source code (lines 1497-1500), where it calls 'math_normal' subroutine to asign normal distribution of dislocation to the simulation domain at initial. However, it achieves a random distributio of the dislocation superimposed on the initial dislocation values say that 'rho_u_ed_neg_0' or 'rho_u_ed_pos_0', etc. What do we need to change to get a non-randon distribution (but has RED line shape) that conforms to this problem?

[MarDiehl]

you can create a microstructure with multiple materials (in you case slices along x) and define for each material a different dislocation density.
Alternatively, create one material, save a restart snapshot, modify the state variables, do a restart. The restart file is in HDF5 format, so modifying it's content is technically not difficult. But you need to understand the state layout (check phase_mechanical_plastic_nonlocal.f90)

[ruanqc]

thank you very much professor for your suggestions, I think the 2nd approach is a good way to obtain this initial condition, since we can use such as hdf5 viewer/ or python to edit the stored dislocation densities in the restart hdf5 file, then redo the simualation based on the modified restart file.

By the way, I have confused that how could we impose a simple shear mechanical boundary conditions and keep the shear stress the same value through the simulation? $\dot{F}_{12}$= const which it can indeed impose a simple shear condition, but the corresponding stress increase with resptect to strain too, could damask grid solver generate costant simple shear stress? I think one of the way is to set two load steps as follow, is it possible/ correct?
thank you

load_shearP12.yaml

---

solver:
mechanical: spectral_basic

loadstep:

• boundary_conditions:
  mechanical:
  dot_F: [[0, x, 0],
  [0, x, 0],
  [0, 0, x]]
  P: [[x, 1609156.61, x],
  [x, 0, x],
  [x, x, 0]]
  discretization:
  t: 0.03
  N: 1
  f_out: 1

• boundary_conditions:
  mechanical:
  dot_F: [[0, x, 0],
  [0, x, 0],
  [0, 0, x]]
  P: [[x, 1609156.61, x],
  [x, 0, x],
  [x, x, 0]]
  discretization:
  t: 500.0
  N: 10000000
  f_out: 5000

[eisenlohr]

The stress (or deformation gradient) values that you specify in the load step are linearly ramped from whatever the corresponding value at the start of the load step happens to be. In your case, I would suggest discretizing the first load step not only with a single increment but finer, since you are going through the (numerically difficult) elasto-plastic transition. You can still do that in a short time, but you need enough spatial discretization to accomplish it.
The second load step then keeps the stress reached in the first load step constant for the given time.

[ruanqc]

The stress (or deformation gradient) values that you specify in the load step are linearly ramped from whatever the corresponding value at the start of the load step happens to be. In your case, I would suggest discretizing the first load step not only with a single increment but finer, since you are going through the (numerically difficult) elasto-plastic transition. You can still do that in a short time, but you need enough spatial discretization to accomplish it. The second load step then keeps the stress reached in the first load step constant for the given time.

I agreed, by increasing the increment at the 1st step so that it can easier to get into plastic state and then remain the same stress level in the 2nd step next. THANK you professor!