Table 2.

Calibrated parameters and prior distribution hyperparameters of stochastic constitutive models for rubber-like material, and the corresponding random nonlinear shear modulus $\hat{\mu }(k_0)$ of (2.12) at k₀=0.1. The parameters are estimated by following the two-step strategy presented in §3.

stochastic model for rubber-like material	calibrated parameters (mean ± s.d.)	calibrated hyperparameters of prior probability distribution	random shear modulus (MPa) (mean ± s.d.)
one-term (two-parameter) Ogden (5.1)	c1=0.5150±0.0263	ρ1=386.3588	$\underset{\_}{\hat{\mu }}(0.1)=0.5145\pm 0.0262$
	α1=0.6748	ρ2=0.0013
one-term Lopez–Pamies (5.2)	c1=0.5207±0.0265	ρ1=385.9715	$\underset{\_}{\hat{\mu }}(0.1)=0.5201\pm 0.0265$
	α1=0.6932	ρ2=0.0013
three-term Yeoh (5.3)	c1=0.5115±0.0256	ρ1=400.0952	$\underset{\_}{\hat{\mu }}(0.1)=0.5112\pm 0.0256$
	c2=−0.0358±0.0001	ρ2=0.0013
b=−0.1	c3=0.0020±0.0001	ξ1=582566
		ξ2=583
		ξ3=10