Dynamically updating Neumann load boundary conditions for Incremental Loading

[RayKruger]

I am modeling large-strain linear elasticity for a cantilever beam using JAX-FEM. In this simulation, I need to dynamically update the Neumann boundary conditions (applied loads) over multiple load steps, incrementally increasing the applied force.

In the plasticity example, I see that Dirichlet displacement boundary conditions can easily be updated dynamically in multiple steps using:

problem.fe.update_Dirichlet_boundary_conditions(dirichlet_bc_info)

where dirichlet_bc_info is structured as:

dirichlet_bc_info = [location_fns, vecs, value_fns]

However, the Neumann bc in the problem class currently only accepts location_fns (position functions) and does not support value functions, making dynamic load updates a little harder.

I implemented a workaround by using the problem.get_surface_maps with the optional argument cell_internal_vars_surface and providing a custom problem.update_load method:

def get_surface_maps(self):
    def surface_map(u, x, cell_internal_vars_surface):
        return np.array([0.0, cell_internal_vars_surface])
    return [surface_map]
                
def update_load(self, new_load):
    for i in range(len(self.internal_vars_surfaces)):
        num_face_quads = self.physical_surface_quad_points[i].shape[0]
        # Create an array of shape (num_face_quads,) filled with new_load
        self.internal_vars_surfaces[i] = (np.full((num_face_quads,), new_load),)

Example of the multi-step Neumann bc I got working:

I also had to adjust the internal JAX-FEM surface_kernel’s jnp.vmap call to match dimensions. This solution is rather hacky and requires digging deep into the internals.

Is there a better way to do this? Could the problem class be extended to support dynamic Neumann bc function updates similar to the Dirichlet boundary condition?

[xwpken]

Hi, it seems that you want to change the magnitude of the applied forces, right? If so, your implementation is correct. But you don't need to change the internal codes, for we have already defined the same variable internal_vars_surfaces, see

jax-fem/jax_fem/problem.py

Line 134 in 8ea5742

self.internal_vars_surfaces = [() for _ in range(len(self.boundary_inds_list))]

You only need to set up the internal_vars_surfaces with the correct format (corresponding to each get_surface_map), and the surface_kernel will get the input.