How to set confining pressure with 3D cylinder in triaxial test

General
1

Hi,
I am now performing deformation analysis on a three-dimensional cylindrical specimen. When performing a triaxial compression test, it is necessary to set a confining pressure on the surface of the cylinder, and the direction of the confining pressure is perpendicular to the cylinder surface inward. I don’t know how to set this force on the cylindrical surface（confine_boundary.mark(boundary_facet_function,1)）. Thank you so much for someone who can help me solve this problem.

Blockquote
from dolfin import *
from mshr import *
from ufl import replace
import numpy as np
import matplotlib.pyplot as plt
#Making a cylindrical geometry
#cylinder = Cylinder(‘coordinate of center of the top circle’, ‘coordinate of center of the bottom circle’, ‘radius of the circle at the top’, ‘radius of the circle at the bottom’)
r1 = 0.025
r2 = 0.025
h1 = 0.0
h2 = 0.1
cylinder = Cylinder(Point(0, 0, h2), Point(0, 0, h1), r1, r2)
geometry = cylinder
#Making Mesh (40 corresponds to the mesh density)
mesh = generate_mesh(geometry, 30)
plot(mesh)
#Boundary Conditions
class ConfineBoundary(SubDomain):
def inside(self, x, on_boundary):
r = np.sqrt(x[0] * x[0] + x[1] * x[1])
return near(r, r1) and between(x[0], (-r1, r1)) and between(x[1], (-r1, r1)) and on_boundary
confine_boundary = ConfineBoundary()
class BottomBoundary(SubDomain):
def inside(self, x, on_boundary):
return near(x[2],h1) and on_boundary
bottom_boundary = BottomBoundary()
class TopBoundary(SubDomain):
def inside(self, x, on_boundary):
return near(x[2],h2) and on_boundary
top_boundary = TopBoundary()
boundary_facet_function = MeshFunction(‘size_t’, mesh, 2)
boundary_facet_function.set_all(0) # from 0
confine_boundary.mark(boundary_facet_function,1)
bottom_boundary.mark(boundary_facet_function,2)
top_boundary.mark(boundary_facet_function,3)
ds = Measure(“ds”)(subdomain_data=boundary_facet_function)

2

Please use proper formatting:

```python
#add code here
```

and please ensure that you include a minimal example. Currently you have provided the mesh only, and no discretization of the underlying PDE.

As you haven’t provided the strong formulation of your system, it is extra hard to Give any guidance