Automatic differentiation interface #8
Description
It would be quite useful for use in FE simulations to have an interface like
σ, state = stress_response(m, strain, args...) that supports eltype(strain) isa Dual to then use an implemented material_response to calculate dσ/deps, and inserts the correct values in a dual σ output.
The key question is how to deal with the state output.
Clearly, for full support, the user would need to provide how this should be differentiated, perhaps in an extended interface like σ, dσ, state, dstate = full_material_response(args...).
An intermediate option is to not provide the derivative of the state, but this will likely cause silent wrong output if the states are used in other calculations.
Another issue is that in coupled simulations (when this would make sense to use) there might be other inputs to the material response functions (e.g. damage) which would be dual numbers, and the output should give the derivatives wrt. this input as well. For these cases, it seems like a usable and general interface isn't realistic and would be too specialized.