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Enhance the stability checks #147

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Merged
merged 2 commits into from
May 21, 2025
Merged

Enhance the stability checks #147

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4fce901
Check stability in all directions
adtzlr May 21, 2025
3052748
Update __about__.py
adtzlr May 21, 2025
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2 changes: 1 addition & 1 deletion src/matadi/__about__.py
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Original file line number Diff line number Diff line change
@@ -1 +1 @@
__version__ = "0.3.0"
__version__ = "0.3.1"
18 changes: 9 additions & 9 deletions src/matadi/_lab_compressible.py
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Expand Up @@ -37,11 +37,11 @@ def stability(stretch, stretches_23):
for j, b in enumerate(c):
B[i, j] = A[(*a, *b)]

# unit force in direction 1
# unit forces in all directions
# calculate linear solution of stretch 1 resulting from unit load
dl = np.linalg.inv(B)[0, 0]
dl = np.diag(np.linalg.inv(B))

return dl > 0
return np.all(dl > 0)

def stress_free(stretches_23, stretch):
s = stress(stretch, *stretches_23)
Expand Down Expand Up @@ -77,11 +77,11 @@ def stability(stretch, stretch_3):
for j, b in enumerate(c):
B[i, j] = A[(*a, *b)]

# unit force in direction 1
# unit forces in all directions
# calculate linear solution of stretch 1 resulting from unit load
dl = np.linalg.inv(B)[0, 0]
dl = np.diag(np.linalg.inv(B))

return dl > 0
return np.all(dl > 0)

def stress_free(stretch_3, stretch):
return [stress(stretch, *stretch_3)[2, 2]]
Expand Down Expand Up @@ -116,11 +116,11 @@ def stability(stretch, stretch_3):
for j, b in enumerate(c):
B[i, j] = A[(*a, *b)]

# init unit force in direction 1
# init unit forces in all directions
# calculate linear solution of stretch 1 resulting from unit load
dl = np.linalg.inv(B)[0, 0]
dl = np.diag(np.linalg.inv(B))

return dl > 0
return np.all(dl > 0)

def stress_free(stretch_3, stretch):
return [stress(stretch, *stretch_3)[2, 2]]
Expand Down
35 changes: 16 additions & 19 deletions src/matadi/_lab_incompressible.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,9 @@
import matplotlib.pyplot as plt
import numpy as np

from ._templates import MaterialHyperelastic
from .math import det


class LabIncompressible:
def __init__(self, material, title=None):
Expand Down Expand Up @@ -47,30 +50,24 @@ def stability(stretch):

P = self.material.gradient([F])[0]
A = self.material.hessian([F])[0]
d2JdFdF = MaterialHyperelastic(lambda F: det(F)).hessian([F])[0]

# hydrostatic stress
p = -P[-1, -1] * kinematics(stretch)[-1]

# convert hessian to (3, 3) matrix
B = np.zeros((3, 3))
c = [(0, 0), (1, 1), (2, 2)]

# convert hessian to (3, 3) matrix and take (2, 2) submatrix
B = np.zeros((2, 2))
delta = np.eye(2)

for i in range(2):
for j in range(2):
B[i, j] = (
A[i, i, j, j]
- delta[-1, j] / kinematics(stretch)[i] * P[-1, -1]
- kinematics(stretch)[-1]
/ kinematics(stretch)[i]
* A[-1, -1, j, j]
+ kinematics(stretch)[-1]
/ kinematics(stretch)[i] ** 2
* P[-1, -1]
* delta[i, j]
)
for i, a in enumerate(c):
for j, b in enumerate(c):
B[i, j] = (A + p * d2JdFdF)[(*a, *b)]

# init unit force in direction 1
# calculate linear solution of stretch 1 resulting from unit load
dl = np.linalg.inv(B)[0, 0]
dl = np.diag(np.linalg.inv(B))

return dl > 0
return np.all(dl > 0)

return (
stress_free(stretch),
Expand Down