Create a new kernel with time derivative of the gradient of coupled variables, such as strain rate.

[Yaode-Yin]

Hello MOOSE expert,
I'm try to couple solid mechanics and the heat conduction. And some coupled terms should be added in the governing equation of heat transfer.
In the new heat equation, I have new terms related to the strain rate. So I think I need a new kernel for this term. So how can I create a new kernel with time derivative of the gradient of coupled variables, such as strain rate or the rate of order parameter?

[GiudGiud]

Hello

Have you followed the tutorial ? There is an example on how to create a new kernel.

The derivative of the gradient of the kernel can be obtained using the Coupleable interface
https://mooseframework.inl.gov/source/interfaces/Coupleable.html
but only for variables. An order parameter is a variable. The strain might be a material property?

[Yaode-Yin]

I changed my strategy to implement the weak form, _F[_qp] *_u[_qp] *_grad_v[_qp]*_grad_v_dot[_qp]*_test[_qp], in MOOSE, where F is a derivative material property. I no longer try to write a generic kernel for the time derivative of the gradient of a coupled variable. Instead just implement my weak form.

Now my codes can be found here: https://github.com/Yaode-Yin/MOOSE_10_11_2024/blob/main/CoupledGradTimeDerivativeKernel.C
https://github.com/Yaode-Yin/MOOSE_10_11_2024/blob/main/CoupledGradTimeDerivativeKernel.h

But in the make process, I still meet some warnings:

/home/Desktop/moose/modules/phase_field/build/header_symlinks/CoupledGradTimeDerivativeKernel.h: In constructor 'CoupledGradTimeDerivativeKernel::CoupledGradTimeDerivativeKernel(const InputParameters&)':
/home/Desktop/moose/modules/phase_field/build/header_symlinks/CoupledGradTimeDerivativeKernel.h:40:34: warning: 'CoupledGradTimeDerivativeKernel::_dFdu' will be initialized after [-Wreorder]
   40 |   const MaterialProperty<Real> & _dFdu;
      |                                  ^~~~~
/home/Desktop/moose/modules/phase_field/build/header_symlinks/CoupledGradTimeDerivativeKernel.h:33:28: warning:   'const VariableGradient& CoupledGradTimeDerivativeKernel::_grad_v_dot' [-Wreorder]
   33 |   const VariableGradient & _grad_v_dot;
      |                            ^~~~~~~~~~~
In file included from /home/Desktop/moose/modules/phase_field/build/unity_src/kernels_Unity.C:56:
/home/Desktop/moose/modules/phase_field/src/kernels/CoupledGradTimeDerivativeKernel.C:27:1: warning:   when initialized here [-Wreorder]
   27 | CoupledGradTimeDerivativeKernel::CoupledGradTimeDerivativeKernel(

I dont understand why these warnings are declared. And how can I fix the code?

[GiudGiud]

in the constructor initialization list, order the attributes in the order as you have them in the header

[Yaode-Yin]

I got it, thanks a lot. I may be close to implement the kernel codes.

[Yaode-Yin]

Hi, GiudGiud. Do you know how to calculate the strain rate as a material property? I look for the material examples in solid mechanics module, but cannot find out related codes.

[GiudGiud]

There are a few examples in the solid mechanics materials. For example:

materials/ComputeIncrementalStrain.C:      _strain_rate[_qp] = _strain_increment[_qp] / _dt;