Table 6.

Sensitivity to stress measurements

Stress type	Stress part	${\rho }_{\mathrm{infl}}^{\mathsf{Wt}}$	${\rho }_{\mathrm{cont}}^{\mathsf{Wt}}$	${\rho }_{\mathrm{infl}}^{\mathsf{C}}$	${\rho }_{\mathrm{cont}}^{\mathsf{C}}$	${\rho }_{\mathrm{infl}}^{\mathsf{WtC}}$	${\rho }_{\mathrm{cont}}^{\mathsf{WtC}}$
1st principal stress	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.536	0.438	0.248	0.343	0.506	0.522
2nd principal stress	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.415	0.290	0.323	0.320	0.495	0.419
3rd principal stress	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.041	0.089	0.192	0.178	0.170	0.186
fiber stress	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.522	0.410	0.252	0.366	0.492	0.517
Stress magnitude	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.578	0.480	0.266	0.370	0.547	0.574
Von Mises stress	${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$	0.552	0.448	0.207	0.290	0.483	0.484
1st principal stress	${\mathit{\sigma }}_{\mathrm{p}}$	0.536	0.310	0.248	0.307	0.506	0.424
2nd principal stress	${\mathit{\sigma }}_{\mathrm{p}}$	0.415	0.288	0.323	0.251	0.495	0.352
3rd principal stress	${\mathit{\sigma }}_{\mathrm{p}}$	0.041	0.273	0.192	0.266	0.170	0.378
Fiber stress	${\mathit{\sigma }}_{\mathrm{p}}$	0.522	0.402	0.252	0.299	0.492	0.471
Stress magnitude	${\mathit{\sigma }}_{\mathrm{p}}$	0.578	− 0.244	0.266	− 0.206	0.547	− 0.322
Von Mises stress	${\mathit{\sigma }}_{\mathrm{p}}$	0.552	0.126	0.207	0.135	0.483	0.171
1st principal stress	${\mathit{\sigma }}_{\mathrm{a}}$	–	0.222	–	0.172	–	0.259
2nd principal stress	${\mathit{\sigma }}_{\mathrm{a}}$	–	0.086	–	0.063	–	0.077
3rd principal stress	${\mathit{\sigma }}_{\mathrm{a}}$	–	− 0.096	–	− 0.034	–	$-$0.067
Fiber stress	${\mathit{\sigma }}_{\mathrm{a}}$	–	0.214	–	0.269	–	0.314
Stress magnitude	${\mathit{\sigma }}_{\mathrm{a}}$	–	0.401	–	0.317	–	0.462
Von Mises stress	${\mathit{\sigma }}_{\mathrm{a}}$	–	0.285	–	0.206	–	0.318
1st principal stress	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.553	0.374	0.249	0.333	0.517	0.483
2nd principal stress	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.388	0.315	0.308	0.280	0.469	0.399
3rd principal stress	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.041	0.145	0.149	0.266	0.133	0.289
Fiber stress	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.532	0.390	0.272	0.358	0.515	0.504
Stress magnitude	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.595	0.456	0.282	0.393	0.569	0.578
Von Mises stress	${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$	0.576	0.375	0.174	0.185	0.474	0.365

Shown is total Cauchy stress (${\mathit{\sigma }}_{\mathrm{p}}+{\mathit{\sigma }}_{\mathrm{a}}$), passive Cauchy stress (${\mathit{\sigma }}_{\mathrm{p}}$), active Cauchy stress (${\mathit{\sigma }}_{\mathrm{a}}$), and total second Piola-Kirchhoff stress (${\mathit{S}}_{\mathrm{p}}+{\mathit{S}}_{\mathrm{a}}$). For each the stress magnitude, first, second, and third principal stress, fiber stress, and von Mises stress is computed. Spearman-$\rho$ values for correlation: inverse of wall thickness ($\mathsf{Wt}$), inverse of curvature ($\mathsf{C}$), inverse of (thickness $\times$ curvature) ($\mathsf{WtC}$) each versus stress at inflation (${\rho }_{\mathrm{infl}}^{\bullet }$) and contraction (${\rho }_{\mathrm{cont}}^{\bullet }$). Active stress is 0 at the point of inflation, hence, results are omitted