Peridynamic Heat Conduction Models

[rbh007720]

Is the Bond-based model able to solve the transient heat transfer problem? In "Thermomechanical peridynamic analysis with irregular non-uniform domain discretization", the implementation is based on an implicit solver for the steady-state problem. Is it possible to treat unsteady-state heat conduction?

Thanks!

[GiudGiud]

@laagesen @bwspenc any ideas on this ?

[jiangwen84]

@rbh007720 have you looked at any PD time derivative kernel?

Let me @hchen139 .

[hchen139]

@rbh007720 I don't think we have implemented any time derivative kernel for PD yet. You can look at the TimeDerivativeNodalKernel to consider the transient heat transfer process.

[rbh007720]

Thanks for the reply. Should I look at TimeDerivativeNodalKernel or TimeDerivative Kernel? I would like to know what is the difference between them.
Thanks!

[hchen139]

TimeDerivativeNodalKernel operates on nodes while TimeDerivative operates on elements. Since PD is a Lagrangian method and uses nodal integration, nodal kernel would make sense for the transient kernel. All the current implementations of PD kernels are based on elemental kernel to use the material classes in other MOOSE modules that are based on FEM.

[GiudGiud]

Nodal kernels are made to solve ODEs that live on individual nodes. So it's quite different from FEM. If you only had nodal kernels, you would only be solving decoupled ODEs on each node. Of course they may be coupled through the values of FEM fields (that have regular kernels for example).
So probably TimeDerivative

[Narayanan1999]

rbh007720 Sir, were you able to do transient analysis in Peridynamics using TimeDerivativeNodalKernel? If so, can you please share the input file or that transient part code?
I tried solving a 1D bar subjected to an initial strain. The transient analysis is done using Newmark-Beta Method from Tensor Mechanics module. Though the input file runs, the values are not matching with theoretical value. The following is the result that I obtained for the displacement occurred at the midpoint of the bar during this time interval (x-time; y-displacment):

[hchen139]

I am not sure whether you can directly run transient analysis based on the available developments in the peridynamics module. There might need some additional developments.

[Narayanan1999]

Ok Sir, Thank you.