ϵlastoPlasm

Description

This project originates from ep2-3De v1.0 and is fully witten in Julia (i.e., the two-languages problem solution). It solves explicit elasto-plastic problems within a finite deformation framework (i.e., adopting logarithmic strains and Kirchoff stresses which allows the use of conventional small-strain stress integration algorithms within a finite deformation framework), using the material point method with cubic b-spline shape functions alongside with a mUSL approach.

• Fig | Slumping dynamics (without any volumetric locking corrections) showing the accumulated plastic strain $\epsilon_p^{\mathrm{acc}}$ after an elastic load of 8 s and an additional elasto-plastic load of $\approx$ 7 s.

The solver relies on random gaussian fields to generate initial fields $\psi(\boldsymbol{x})$, e.g., the cohesion $c(\boldsymbol{x}_p)$ or the internal friction angle $\phi(\boldsymbol{x}_p)$, with $\boldsymbol{x}_p$ the material point's coordinates.

• Fig | Initial cohesion field $c_0(\boldsymbol{x}_p)$ with average $\mu=20$ kPa with a variance $\sigma\pm5$ kPa.

Content

1. Usage

Usage

Structure of the project

The general structure is simple. The ./scripts folder contains two sub-folders, i.e., ./program and ./unit_testing.

The ./src folder contains all functions needed, which are called by the different programs located in ./scripts. The ./docs/out folder contains all the plots and data generated by the solver during computation. If needed, modifications can be made to these routines by changing initial parameters and/or algorithm blocks.

ϵp2DeJu Lumos !

.
├── Manifest.toml
├── Project.toml
├── README.md
├── docs
│   ├── img
│   ├── out
│   └── refs
├── license
├── scripts
│   ├── program
│   │   └── ep23De.jl
│   └── unit_testing
│       ├── allocTest.jl
│       ├── kwargsTest.jl
│       └── shpfunTest.jl
├── src
│   ├── ep2DeJu.jl
│   ├── fun_fs
│   │   ├── elastoplast.jl
│   │   ├── mapsto.jl
│   │   ├── plast.jl
│   │   ├── shpfun.jl
│   │   └── solve.jl
│   ├── misc
│   │   ├── doc.jl
│   │   ├── physics.jl
│   │   ├── plot.jl
│   │   ├── rxiv
│   │   ├── setup.jl
│   │   ├── types.jl
│   │   └── utilities.jl
│   └── superInclude.jl
└── start_macOS.sh

How to plasmazing ?

0. (opt.) Get Julia here and follow instructions for installation
1. cd to the local repo ./ep2DeJu
2. Launch Julia (on macOS, drag & drop start_macOS.sh in the terminal)

% julia --project  
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.6.5 (2021-12-19)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

3. Enter pkg mode ], then activate . the project ep2DeJu and instantiate its environment and related packages. You can st to check package status.

(ep2DeJu) pkg> activate .
(ep2DeJu) pkg> instantiate 
(ep2DeJu) pkg> st
Project ep2DeJu v0.1.0
Status `./ep2DeJu/Project.toml`
  [6e4b80f9] BenchmarkTools v1.3.2
  [b964fa9f] LaTeXStrings v1.3.0
  [91a5bcdd] Plots v1.39.0
  [92933f4c] ProgressMeter v1.9.0
  [37e2e46d] LinearAlgebra
  [44cfe95a] Pkg v1.8.0

(ep2DeJu) pkg>

4. Code include() and execute method ϵp23De(nel,varPlot,cmType; kwargs...). It should result in the following:

julia> include("./scripts/program/ep23De.jl")
ϵp23De (generic function with 1 method)
julia> L = [64.1584,12.80]
julia> ϵp23De(L,40,"P","MC")
[ Info: ** ϵp2De v0.3.0: finite strain formulation **
┌ Info: mesh & mp feature(s):
│   nel = 528
│   nno = 585
└   nmp = 591
[ Info: launch bsmpm calculation cycle...
✓ working hard:          Time: 0:00:09 (22.83 ms/it)
  nel,np:        (528, 591)
  iteration(s):  432
  ηmax,ηtot:     (21, 849)
  (✓) t/T:       100.0
┌ Info: Figs saved in
└   path_plot = "./docs/out/"
│
└ (✓) Done! exiting...
julia>

5. Input parameters: L is a vector of the Eulerian mesh dimensions $\ell_{x,z|x,y,z}$ (two- and three-dimensional geometries are now supported since v0.3.0), the argument nel defines the elements along the $x$ dim., varPlot defines state variable to be displayed in plot ("P" for pressure, "du" for displacement or "epII" for plastic strain), and cmType defines the constitutive model being used.

6. Optional kwargs are: shpfun={:smpm,:gimpm,:bsmpm} defining shape functions, fwrk={:infinitesimal,:finite} defining the deformation framework, trsf={:picflipUSL,:mUSL,:tpicUSL} defining the mapping scheme, vollock={true|false} is a boolean controlling volumetric locking corrections using the $\Delta\bar{F}$ method (see [1,2]), and GRF={true|false} is a boolean switching on/off gaussian random cohesion fields (see [3,4]). An illustrative example with kwargs is given below

ϵp23De([64.1584,12.80],40,"P","MC";shpfun=:bsmpm,fwrk=:finite,trsf=:mUSL,vollock=true)

7. Outputs (figs, gif, etc.) are saved in the folder ./docs/out/

8. (final note): ϵp23De automatically infers whether the two- or three-dimensional solver should be compiled, solely based on the dimension of L, i.e., length(L)={2|3}.

References

For useful references, the reader can have a look in the folder ./docs/refs, where some of the following references can be found

1. Xie M., Navas P., López-Querol S. An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling. Int J Numer Anal Methods Geomech. 2023;1-21. https://doi.org/10.1002/nag.3599

2. Zhao Y., Jiang C., Choo J. Circumventing volumetric locking in explicit material point methods: A simple, efficient, and general approach. Int J Numer Methods Eng. 2023;1-22. https://doi.org/10.1002/nme.7347

3. Räss, L., Kolyukhin D., and Minakov, A. Efficient parallel random field generator for large 3-D geophysical problems. Computers & Geosciences. 2019;158-169. https://doi.org/10.1016/j.cageo.2019.06.007

4. Ma, G., Rezania, M., Mousavi Nezhad, M. et al. Uncertainty quantification of landslide runout motion considering soil interdependent anisotropy and fabric orientation. Landslides 12022:1231–1247. https://doi.org/10.1007/s10346-021-01795-2