Stress gradient calculation

This demo shows the stress gradient calculation module. A gradient is calculated by fitting a plane into a node and its neighbor nodes of an FEM mesh.

See documentation for details on the module.

import numpy as np
import pandas as pd

import pylife.stress.equistress
import pylife.mesh.gradient
import pylife.vmap

import pyvista as pv

Read in demo data and add the stress tensor dimensions for the third dimension.

vm_mesh = pylife.vmap.VMAPImport("plate_with_hole.vmap")
mesh = (vm_mesh.make_mesh('1', 'STATE-2')
               .join_coordinates()
               .join_variable('STRESS_CAUCHY')
               .to_frame())

Calculate and add von Mises stress

mesh['mises'] = mesh.equistress.mises()

Calculate stress gradient on von Mises stress

grad = mesh.gradient.gradient_of('mises')
grad["abs_grad"] = np.linalg.norm(grad, axis = 1)
mesh = mesh.join(grad)
display(mesh)

		x	y	z	S11	S22	S33	S12	S13	S23	mises	dmises_dx	dmises_dy	dmises_dz	abs_grad
element_id	node_id
1	1734	14.897208	5.269875	0.0	27.080811	6.927080	0.0	-13.687358	0.0	0.0	33.996987	-1.893361	3.568289	0.0	4.039493
	1582	14.555333	5.355806	0.0	28.319006	1.178649	0.0	-10.732705	0.0	0.0	33.399850	-1.508279	3.797076	0.0	4.085669
	1596	14.630658	4.908741	0.0	47.701195	5.512213	0.0	-17.866833	0.0	0.0	54.777007	-1.442228	5.469620	0.0	5.656568
	4923	14.726271	5.312840	0.0	27.699907	4.052865	0.0	-12.210032	0.0	0.0	33.446991	1.381062	6.028931	0.0	6.185091
	4924	14.592996	5.132274	0.0	38.010101	3.345431	0.0	-14.299768	0.0	0.0	44.070962	-0.538004	-5.162114	0.0	5.190074
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
4770	3812	-13.189782	-5.691876	0.0	36.527439	2.470588	0.0	-14.706686	0.0	0.0	43.577209	0.489075	-5.247270	0.0	5.270013
	12418	-13.560289	-5.278386	0.0	32.868889	3.320898	0.0	-14.260107	0.0	0.0	39.903508	-0.352899	-9.819771	0.0	9.826110
	14446	-13.673285	-5.569107	0.0	34.291058	3.642457	0.0	-13.836027	0.0	0.0	40.478974	3.865992	-7.135043	0.0	8.115093
	14614	-13.389065	-5.709927	0.0	36.063541	2.828889	0.0	-13.774759	0.0	0.0	42.140169	0.252531	-5.859227	0.0	5.864667
	14534	-13.276068	-5.419206	0.0	33.804211	2.829817	0.0	-14.580153	0.0	0.0	41.143837	-0.134343	-10.059937	0.0	10.060834

37884 rows × 14 columns

grid = pv.UnstructuredGrid(*mesh.mesh.vtk_data())
plotter = pv.Plotter()
plotter.add_mesh(grid, scalars=mesh.groupby('element_id')["abs_grad"].mean().to_numpy(), show_edges=True, cmap='jet')
plotter.add_scalar_bar()
plotter.show()

"That's it"

"That's it"