Tissue Mechanics Assessment: Unconfined Compression of biphasic and viscoelastic media

Body tissues are often modelled as being viscoelastic or biphasic. Since cellular activity depends on the mechanical environment, it is important to understand the mechanics of each type of material. You are required to submit a short report (no more than 1000 words and 8 figures) on the unconfined compression of biphasic and viscoelastic media. Using FEBio, please analyse the mechanics (stress, strain, fluid pressure etc.) of a 10 mm diameter and 3mm height cylindrical tissue in unconfined compression. You should compare two different materials:

1. Biphasic: The material should have an isotropic elastic solid phase, defined by E = 100 MPa, v=0.3, and a constant permeability of 1 x 10^-15 m⁴/Ns. Take solid volume as 0.2.

2. Viscoelastic: The material should be based on isotropic elasticity, defined by E = 100 MPa, v=0.3. Coefficient G1 should be 0.5 and relaxation time t1 = 100. All other parameters should be left at their default values (G2-G6 = 0, t2-t6 = 1).

In class, it was shown that the relaxation modulus for a 3 parameter solid may be written as

Y(t) = A₀ + A₁e^-t/τ_1.

This may be expressed as:

Y(t) = A₀ [1 + (A₁/A₀)e^-t/τ_1] = E [1 + G1e^-t/τ_1]

where A0 = E, A₁/A₀ = G1 and τ₁ = t1. The value of G1 and t1 have been chosen to approximately make the time history of the axial stress similar to that of the biphasic tissue. Please note they will not match perfectly.

Each cylinder of material should be subjected to axial unconfined compression to -0.1 strain at -0.01 s^-1 by an impermeable, rigid platen. You are required to analyse, compare and contrast the mechanics of each material in the ramp phase and until equilibrium.

Your report should contain the following sections:

Introduction: Provide a very brief introduction. The introduction should finish with precise aims and objectives of the activity.

Methods: The methods section should fully describe your model. Include information regarding the mesh, materials, boundary and loading conditions along with anything else you think relevant.

Results: Use appropriate figures to help you describe the mechanics of each material in unconfined compression. Every figure must be cited and described in the text, highlighting the important aspects of the figure.

Discussion: Compare and contrast the materials and discuss the implications of this difference when describing the cellular stress environment.

Conclusion: A short conclusion will suffice.

You should submit your report and two .feb files: one for the viscoelastic material and one for the poroelastic medium.

PLEASE NOTE:

• There is not one perfect model. Many models will achieve the aim, but some will be better than others.

• The more nodes and elements you have, the longer the solution time. The smaller the element size, the more accurate the solution. However, too many and you may be waiting hours/days for a solution. Think about how to use symmetry to reduce the problem's geometry.

• You can use a bias in your mesh, if you wish, to concentrate nodes and elements in regions of steep gradients of fluid pressure.