it will be possible to assess the real accuracy error of the methodology which, however, cannot be lower than 0.002%. Tab.5 Results for the real experiment: Mooney-Rivlin constatns c10 and c01, equivalent Young’s modulus Eeq(R) MR and its accuracy error respect to the equivalent Young’s modulus Eeq. T determined by standard tensile tests Result (MPa) Error (%) c10 c01 Eeq(R) MR Eeq(R) MR Number of Iterations GR(0) 1 0.022328 0.045222 0.405299 2.607 120 GR(0) 2 0.022381 0.045171 0.405316 2.612 124 GR(0) 3 0.022327 0.045223 0.405298 2.607 154 GR(0) 4 0.022368 0.045183 0.405308 2.610 87 GR(0) 5 0.022295 0.045253 0.405287 2.604 110 GR(0) 6 0.022335 0.045216 0.405301 2.608 125 GR(0) 7 0.022422 0.045131 0.405318 2.612 158 GR(0) 8 0.022341 0.045210 0.405301 2.608 127 GR(0) 9 0.022354 0.045197 0.405302 2.608 82 GR(0) 10 0.022329 0.045221 0.405298 2.607 86 GR(0) 11 0.022401 0.045151 0.405314 2.611 81 GR(0) 12 0.022421 0.045133 0.405323 2.613 117 GR(0) 13 0.022424 0.045130 0.405325 2.614 64 GR(0) 14 0.022322 0.045227 0.405296 2.607 73 GR(0) 15 0.022313 0.045236 0.405292 2.606 113 GR(0) 16 0.022378 0.045174 0.405315 2.611 80 GR(0) 17 0.022348 0.045203 0.405303 2.608 85 GR(0) 18 0.022429 0.045125 0.405325 2.614 70 GR(0) 19 0.022307 0.045242 0.405294 2.606 74 GR(0) 20 0.022375 0.045176 0.405308 2.610 90 Mean 0.022360 0.045191 0.405306 2.609 101 SD/Mean (%) 0.19 0.09 0.0028 CONCLUSION Results demonstrate that a mixed experimental/numerical method using non-destructive indentation is a reliable and accurate technique for characterization of Mooney-Rivlin incompressible material models. Assuming a priori, according to literature, to employ phenomenological hyperelastic constitutive laws to characterize soft biological tissues, this study demonstrate that the analyzed technique has the potential to be extended to in-vivo and ex-vivo tissues. Clinical studies, based on the collection of material parameters c10 and c01 of human soft tissues characterized by specific pathologies, age and living conditions, etc., could be carried on. Benchmark and experimental studies demonstrated that the methodology can be used to estimate more than one material parameter. The reported results allow to state firmly that the modified Nelder-Mead algorithm MNMA allowed to performing non-destructive material characterization of rubber-like materials using a single experimental procedure. A further 29
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