Confined compression test
The specimen dimensions used for these tests are w=6.35 mm and h=1.78 mm. Material properties corresponding to a normal human cartilage were used, modulus of elasticity E=0.675 MPa, Poissonís ratio ν=0.125, fluid fraction ratio θf=0.83, permeability coefficient κ=7.6◊10-15 m4N-1s-1. Confined compression is a sample placed in a confining chamber and compressed with a permeable piston. The problem is one dimensional in y.
Unconfined compression test
The specimen dimensions and material constants used for these tests are the same as in case of confined compression test. Unconfined compression is a sample of material placed between two platens without side constraints. The platens may be perfectly lubricated or perfectly adhesive (Figure). In case of perfectly lubricated problem the deformation might be expected to be independent of y; thus the problem becomes one dimensional problem in x.
In both cases, the specimen is subjected to the ramp loading. The prescribed displacement is increased linearly in time to reach the prescribed deformation of 5% at instant t0=500 s, i.e. ū=0.089 mm in the confined compression test, and ū=0.0445 mm in the unconfined compression test. The results were obtained with a regular mesh of 2x2 elements, in a single time step Δt=tmax=1000 s.
Indentation test
The specimen dimensions and material constants used for this test are the same as in previous cases. During this indentation test, the sample is compressed with a plane-ended impermeable indenter. The prescribed displacement is ū=0.089 mm. The loading conditions are the same as before. More refined mesh of 3x2 elements was used.
All the previous tests are so-called stress-relaxation tests. A creep test is also often performed in order to obtain material properties of a cartilage. At a time t0, a solid phase of the specimen, the indenter is considered to be permeable, is loaded with a constant stress that is maintained for a sufficiently long time period (1000 s). Two different loading histories were applied. The prescribed value of the loading stress is increased linearly in time until t0=500 s while in the other case the stress reaches its prescribed value τ=-100 Pa suddenly at instant t0=10 s. Same material constants, dimensions and mesh refinement as in previous indentation test were used.


Confined compression test:
Displacements: Solid ux≈0 Solid uy Fluid ux≈0 Fluid uy Vector form
Stresses: σxx σyy σxy≈0 Pressure
Unconfined compression test with lubricated platens:
Displacements: Solid ux Solid uy Fluid ux Fluid uy Vector form
Stresses: σxx σyy σxy≈0 Pressure
Unconfined compression test with adhesive platens:
Displacements: Solid ux Solid uy Fluid ux Fluid uy Vector form
Stresses: σxx σyy σxy Pressure
Stress-relaxation indentation test:
Displacements: Solid ux Solid uy Fluid ux Fluid uy Vector form
Stresses: σxx σyy σxy Pressure
Creep indentation test with linearly increased loading stress:
Displacements: Solid ux Solid uy Fluid ux Fluid uy Vector form
Stresses: σxx σyy σxy Pressure
Creep indentation test with step constant loading stress:
Displacements: Solid ux Solid uy Fluid ux Fluid uy Vector form
Stresses: σxx σyy σxy Pressure

Comments:

Marc:
A wonderful job. Super helpful information.

Sandra:
How neat! Is it raelly this simple? You make it look easy.

Anonym:
You write very well!

name:

email (will not be published):

the value of 𝛑 to two decimal places:

message (required):