Integration variables derivatives in generalised behaviours

[mhpierre]

Dear Thomas,

I'm working with thermoporoplasticity in MFront, and I have a small interrogation about the calculation of derivatives of the integration variables with respect to the external variables. From what I understand, there are two possible ways to do it:

• By calling the blocks of the invert of the Jacobian iJ_x_y directly and calculating "by hand",
• By using the getIntegrationVariablesDerivatives method.

I have an elastic strain and a plastic multiplier, I define the right derivatives of the implicit equations with respect to the external variables, as so:

∂fε_el∕∂Δεᵗᵒ = - I₄ ;
∂fλₚ∕∂Δpₗ  = (β-b)⋅∂f∕∂p / (E⋅E);
∂fλₚ∕∂ΔT    = -κ ⋅∂f∕∂p / (E⋅E);

where other derivatives are zero.
For the first solution, it works as intended:

Stensor4 ∂Δε_el∕∂Δεᵗᵒ = -( iJ_ε_el_ε_el ⋅∂fε_el∕∂Δεᵗᵒ ) ;
Stensor ∂Δε_el∕∂Δpₗ  = -( iJ_ε_el_λₚ ⋅∂fλₚ∕∂Δpₗ ) ;
Stensor ∂Δε_el∕∂ΔT  = -( iJ_ε_el_λₚ ⋅∂fλₚ∕∂ΔT ) ;

However if I use the getIntegrationVariablesDerivatives method, as so:

Stensor4 ∂Δε_el∕∂Δεᵗᵒ ;
Stensor  ∂Δε_el∕∂Δpₗ ;
Stensor  ∂Δε_el∕∂ΔT ;
        
getIntegrationVariablesDerivatives_εᵗᵒ(∂Δε_el∕∂Δεᵗᵒ);
getIntegrationVariablesDerivatives_pₗ(∂Δε_el∕∂Δpₗ);
getIntegrationVariablesDerivatives_T(∂Δε_el∕∂ΔT);

I get a warning on compilation that variables ∂fλₚ∕∂Δpₗ and ∂fλₚ∕∂ΔT are being set but not used. Am I misunderstanding the way getIntegrationVariablesDerivatives works?

[thelfer]

Those variables are views to blocks of a zero initialized matrix. If those derivatives are null, you don't need to use those variables. In this case, you can explicitly discard them as follows:

static_cast<void>(∂fλₚ∕∂Δpₗ);