All three parameters were evaluated at the yield threshold and showed fairly constant values irrespective of the mechanical history.
The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez Moreno) to discretize the problem.
To avoid the stress singularity, we introduce a yield threshold in the brittle ductile transition near the down-dip edge of the fault.
The penetration distances measured both at the first yield threshold and the following one, which represent the thicknesses of the upper and lower layers, are close to the width of jump (wm) in the case of DSPC monolayer.
The same phenomenon was also found in the case of DPPC and DLPC bilayers at different temperatures by Sergi et. al., which explores the significant impact of ions on the yield threshold force of lipid film.
The indentation force curve of the film in AFM tip approaching process is similar to that of DSPC (shown in Figure 2B), where there is also a yield threshold marked by a black arrow.
In addition, the break through force at the yield threshold and the measured thickness values with AFM are related to several experimental parameters, such as the cantilever spring constant, the shape and size of the used AFM tip.
The yield threshold forces of DMPC are about 2 nN (Figure Eight A in reference [14]) in buffered water solution (fl) at 30°C, which is much smaller than that in buffered high ionic strength solution (about 4.7nN (fh), fl is equal to 0.43 times of fh).
Table 2 demonstrates that increasing the [Na+] to 0.63 M enables the 95% radiochemical yield threshold to be reached within a shorter time (maximum 75 min for the proteins used here), after which a purification step is not required prior to its in vivo use.
Indentation force curves of DSPC monolayer film were obtained at different sites of the film without defect, and an example of indentation force curve is described in Figure 2B where there is a yield threshold [13] denoted by a black arrow.
This conclusion could be used to explain the small yield threshold force of DSPC bilayer (lower layer covered with upper layer) obtained in our work (0.79 ± 0.39 nN) compared with that of DMPC or DPPC at the same temperature (Figure Eight A in reference [14]) considering that our experiment was conducted under the deionized water condition.
