Fig. 5.

Proposed CF combination for unique parameter estimation emerging from the in silico analysis. a The landscape of the $|\mathrm{\Delta }\mathit{u}|$ CF (residual in mm), which is the chosen geometric CF (see Sect. 2.4 for more details). b Landscape of the energy-based CF. A straight line pattern emerges that demonstrates the independence of the CF on $C_1$ and its ability to uniquely identify $\mathit{\alpha }$. c Unique parameter estimation with the combined use of the energy-based CF for $\mathit{\alpha }$ parameter identification and the $L^2$ displacement norm CF. A superimposed black curve is fitted to the parameter combinations corresponding to the minimum $|\mathrm{\Delta }\mathit{u}|$ CF residual values. The horizontal black line corresponds to the minimum energy-based CF residual. The identified parameters (indicated by the black circle at the intersection of the energy-based and geometry-based CF minimization lines) coincide with the ground truth values ($\mathit{\alpha }=30$, $C_1=1000\text{Pa}$). (Minimum and maximum CF residuals are shown in blue and red, respectively.)