Indenteur, plat (D = 12.5 mm)

(En anglais seulement) This tool allows for the computing and visualizing of the shear modulus (MPa) from an unconfined compression test performed using a flat indenter on a spherical sample (Figure 1).

Results analysis is performed considering small deformation of a perfectly spherical sample (with uniform elastic material properties) tested in unconfined compression between two flat platens. Curve fitting is based on Gauthier et al., 2004 who used the Hertz model predicting the force exerted by a rigid spherical body under small deformation (less than 10%) which is given by the equation (attached), where F(r) is the force exerted by the sphere when the distance separating the compressing platen surface from the bottom platen is r (and r ˂ 2 R₀), u is the shear modulus and R₀ is the bead's initial radius.

Mach-1 Analysis – Modèle élastique sur échantillon sphérique – paramètres

Mach-1 Analysis – Modèle élastique sur échantillon sphérique – Equation

Mach-1 Analysis – Modèle élastique sur échantillon sphérique – Exemple

(En anglais seulement) This tool allows for the computing and visualizing of the fibril network modulus (MPa), the equilibrium modulus (MPa), the permeability (mm²/MPa·s), and the mean square error (RMSE) of the fit calculated from a “Stress Relaxation” curve (load or force vs. time) in unconfined compression (Figure 1) on a disk or osteochondral core sample. The curve is fitted to the linear fibril-network-reinforced biphasic model (Soulhat et al. 1999) in order to obtain the mechanical properties of the disk. Sample radius, strain, and Poisson’s ratio need to be specified. This model is well adapted for the mechanical description of samples containing a liquid fraction and a fibril network, for example: cartilage or gel samples. A user license is required in order to obtain the results of the poroelastic model in unconfined compression (Software Add-On, contact Biomomentum to obtain your license).

The nonhomogeneous composite model (i.e. linear fibril-network-reinforced biphasic model) is an extension of the previously developed isotropic homogeneous biphasic model, and was achieved by reinforcing the latter with a network of nonlinear fibrils distributed homogeneously in the r, θ, z directions and which resist extension only (Figure 2). The isotropic matrix is described by the drained elastic constants E_m (Young’s modulus), v_m(Poisson’s ratio) and a hydraulic permeability k. The fibril network is described by the Young’s modulus of individual fibrils e_f which, combined with a fibril volume fraction χ (fibrils volume/ total-volume), results in an equivalent tensile modulus of the fibril network, E_f = 1/3 χ e_f (since 1/3 of the fibrils are oriented in each of three mutually orthogonal directions).

For example, (Figure 3) shows parameters used for the “Stress Relaxation” function in an unconfined compression testing protocol on ovine cartilage disks. Corresponding results are shown in (Figure 1).

Mach-1 Analysis – Modèle poroélastique en compression non-confinée – Paramètres

Mach-1 Analysis – Modèle poroélastique en compression non-confinée – Cartilage

Mach-1 Analysis – Modèle poroélastique en compression non-confinée – Exemple