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")
pyLife_mesh = (vm_mesh.make_mesh('1', 'STATE-2')
               .join_coordinates()
               .join_variable('STRESS_CAUCHY')
               .join_variable('DISPLACEMENT')
               .to_frame())

Calculate and add von Mises stress

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

Calculate stress gradient on von Mises stress

# pyLife_mesh["grad"] = pyLife_mesh.gradient.gradient_of('mises')
grad = pyLife_mesh.gradient.gradient_of('mises')

pyLife_nodes = pd.concat([pyLife_mesh.groupby('node_id').mean(), grad], axis=1)
pyLife_nodes["abs_grad"] = np.linalg.norm(grad,axis = 1)
display(pyLife_nodes)

	x	y	z	S11	S22	S33	S12	S13	S23	dx	dy	dz	mises	dx	dy	dz	abs_grad
node_id
1	7.900000	0.000000	0.0	-0.802995	-68.944250	0.0	-1.869146	0.0	0.0	5.717073e-03	3.114637e-36	0.0	68.842539	-5.616596	5.359001	0.0	7.763056
2	20.000000	0.000000	0.0	30.042272	24.801415	0.0	-0.092955	0.0	0.0	6.448063e-03	6.655135e-38	0.0	27.796941	-0.915970	-0.225004	0.0	0.943201
3	20.000000	9.000000	0.0	30.024656	0.024460	0.0	0.005555	0.0	0.0	5.691581e-03	1.163137e-04	0.0	30.012435	-0.000519	-0.000082	0.0	0.000526
4	0.000000	9.000000	0.0	18.584425	-0.299882	0.0	5.858656	0.0	0.0	-3.303485e-36	-5.751588e-03	0.0	24.948312	0.122343	-0.613853	0.0	0.625926
5	0.000000	6.300000	0.0	216.279488	5.181528	0.0	-6.305715	0.0	0.0	1.365477e-35	-5.435489e-03	0.0	215.130796	16.186186	1.395853	0.0	16.246262
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
14610	-6.424311	-6.312416	0.0	52.471514	-6.999632	0.0	-3.310140	0.0	0.0	-3.627928e-03	1.724823e-03	0.0	56.589972	1.880459	-4.367367	0.0	4.755000
14611	-11.206949	-2.616344	0.0	10.610512	-1.571398	0.0	-10.754698	0.0	0.0	-5.765039e-03	4.447560e-05	0.0	21.879599	-0.800229	-6.246270	0.0	6.297321
14612	-13.101126	-7.120056	0.0	46.328791	1.005923	0.0	-11.133379	0.0	0.0	-4.997560e-03	1.022665e-04	0.0	49.725466	0.651738	-5.209006	0.0	5.249620
14613	-10.574732	-4.750605	0.0	27.268641	-2.193988	0.0	-15.060814	0.0	0.0	-5.150582e-03	1.811491e-04	0.0	38.583754	0.381298	-6.330618	0.0	6.342090
14614	-13.389065	-5.709927	0.0	36.637676	3.454111	0.0	-14.996684	0.0	0.0	-5.329776e-03	2.166348e-05	0.0	43.646014	-0.540695	-6.376289	0.0	6.399172

14614 rows × 17 columns

mesh = pv.PolyData(pyLife_nodes[['x', 'y', 'z']].values)
mesh.point_arrays["abs_grad"] = pyLife_nodes["abs_grad"].values
mesh.plot(scalars="abs_grad",log_scale = False)