Hyper-elastic membranes
(Application in soft tissue biomechanics)
The goal of this problem is to simulate by FEA the inflation of a hyper-elastic membrane as shown in the figure below
Input of the problem:
The membrane is in Neo-Hookean material, C10=0.1 MPa, D=10 MPa
The membrane is a disc with radius = 15mm clamped on its circular edge. Its thickness is equal to 1mm. An inflation pressure = 20 kPa is applied.
Question 1.
By modelling the membrane with linear shell elements with 4 nodes (as for instance in the figure below), find the vertical displacement at the centre as well as the stresses in the middle plane of the membrane at the centre. Use the symmetries to simplify the model.
Use the mesh size = 0.5mm (verify the convergence).
Study the influence of the boundary conditions (clamped vs free rotations)
Question 2.
Run now an axisymmetric model as illustrated below.
Mesh using bilinear axisymmetric plane elements with 4 nodes per element. Use 5 elements in the thickness (if necessary verify the convergence).
Calculate the vertical displacement and the stress at the center for 3 pressures indicated in the figure.
Study the influence of boundary conditions (clamped vs free rotations)
Question 3.
Apply now a pinch in the extremities of the membrane so as to realise the clamping as shown below.
Simulate this pinch as a preliminary computation step by using contact elements with a Coulomb’s law, with the friction coefficient equal to 0.3.
Compute then the displacement and the stress at the centre for the 3 pressures shown in the figure.
Compare the obtained results with previous solutions.
Question 4.
Increase the pressure until you reach an instability
Include collagen fibers in the material to avoid the instability
