Biomedical Engineering Reference
In-Depth Information
2
Objective
A fundamental building block for developing a structural model capable of
simulating pulmonary alveolar recruitment manoeuvres is an element of contact
with adhesion caused by the surface tension. A constitutive equation for this element
is proposed and evaluated numerically in a simple structure using the non-linear
finite element method.
3
Methodology
A constitutive equation for the contact with adhesion finite element is formulated. In
order to validate this model a simulation of the contact between a simplified mem-
brane and a undeformable surface is conducted. This simulation is performed with
the finite element method (FEM). Because problems involving large deformations,
rotations, and particularly contact are not linear, an algorithm for finding equilibrium
configurations had to be used. Since the contact element's constitutive equation
introduce critical points to the system, the arc-length method was implemented to
avoid numerical instabilities.
3.1
Constitutive Equation
The adhesive contact model developed here is simplified. The surface tension
is considered constant and the geometry of the meniscus is approximated. The
formulation is based on a number of assumptions announced below, which are
illustrated in the Fig. 3 .
h1. The liquid film is continuous on both membrane surfaces. At height h
from the surface, molecular attraction forces start to be significant (see
Fig. 3 g). At greater distances, d>2h, the attraction forces are negligible.
h2. At a distance d
d 2 the liquid films begin to attract each other (see
Fig. 3 b) and a meniscus is formed between both surfaces (see Fig. 3 c).
h3. The pressure inside the meniscus (or on the contact region) is stated by
the Young-Laplace Law [ 18 ],
2h
D
1
:
1
r 2
p YL D
r 1 C
(1)
h4. The surface of the meniscus has two curvature radii, but only the one
proportional to distance is considered r
D
r 1
D
d=2 (see Fig. 3 d).
(continued)
 
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