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https://github.com/hariprasadr1hp/fem_matlab

A Matlab program which solves a static nonlinear FEM problem with linear shape functions, for an ideal elastic-plastic material
https://github.com/hariprasadr1hp/fem_matlab

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A Matlab program which solves a static nonlinear FEM problem with linear shape functions, for an ideal elastic-plastic material

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# FEM (Matlab/Octave)

A Matlab/Octave program which solves a static nonlinear FEM problem with linear
shape functions, for an ideal elastic-plastic material. Stress-Distribution,
elastic and plastic regimes, convergence crteria are generated

### How to run?

```bash
make
```

### Files:

- `input.m` :: The file to start with
- `ElastoPlastic.m` :: The file to calculate elastic + plastic strains
- `Elastic.m` :: The file to calculate elastic convergence
- `ElementRoutine.m` :: to determine J, B, N matrix values
- `MaterialRoutine.m` :: Material routine for elastic ideal-plastic material
- `exact.m` :: to calculate the analytical solution

### Procedure

Change the value in of 'mode' to either '1' or '2' in `Input.m` file to switch
between:

- `mode = 1` -> for calculating elastic convergence,
- `mode = 2` -> for calculating elastic + plastic strains

Can also modify the other parameters based on the needs:

- elements
- yield stress, E, Nu
- inner/outer radius
- Gauss points
- time-step

### Plots

- ![Convergence Study in Elastic Regime](Plots/1_Convergence%20Study%20in%20Elastic%20Regime.png)
- ![widening of outer radius b over time](Plots/2_widening%20of%20outer%20radius%20b%20over%20time.png)
- ![$\sigma_{rr}$ Distribution](Plots/3_sigmarrdistribution.png)
- ![$\sigma_{\phi \phi}$ Distribution](Plots/4_sigmaphiphidistribution.png)
- ![Displacement Distribution $u$ at $t=1$](Plots/5_Displacement%20distribution%20u%20at%20tequals1.png)