Hi, I am trying to caculate for a given stress the corresponding strain in the Von Mises plasticity example. I know that this results in a non-linear equation.

Not notice I have the following equations:

```
σᵗ = C ⊡ (ϵ - ϵᵖ)
J₂ = 0.5 * dev(σᵗ) ⊡ dev(σᵗ) # second invariant
σᵗₑ = sqrt(3.0*J₂) # effective trial-stress (von Mises stress)
σʸ = σ₀ + H * k
φᵗ = σᵗₑ - σʸ # Trial-value of the yield surface
h = H + 3*G
μ = φᵗ / h # plastic multiplier
c1 = 1 - 3G * μ / σᵗₑ
s = c1 * dev(σᵗ) # updated deviatoric stress
σ = s + vol(σᵗ) # updated stress
```

The only thing which I have not given is \epsilon. Now I reordered and substitute everything:

```
σ = (1 - 3G*((sqrt(1.5*dev(C ⊡ (ϵ - ϵᵖ)) ⊡ dev(C ⊡ (ϵ - ϵᵖ))) - (σ₀ + H * k) ) / (H + 3*G) )/ (sqrt(1.5* dev(C ⊡ (ϵ - ϵᵖ)) ⊡ dev(C ⊡ (ϵ - ϵᵖ))))) * dev(C ⊡ (ϵ - ϵᵖ)) + vol(C ⊡ (ϵ - ϵᵖ))
```

Is there a “nice” way to solve this equation somehow?