Table 4.

Estimated parameters from proposed multi-step optimization procedure

Parameter	True value	Case 1	Case 2	Case 3	Case 4	Parameter range
$a$(kPa)	0.236	0.236	0.236	0.238	0.238	$(0.1,2)$
$b$	10.81	10.75	10.74	10.61	10.67	$(1,30)$
$a_{\text{f}}$(kPa)	20.03	19.96	19.54	19.97	18.97	$(1,30)$
$b_{\text{f}}$	14.15	14.38	15.97	15.29	18.45	$(1,25)$
$a_{\text{s}}$(kPa)	3.72	3.91	3.83	4.27	4.08	$(0.1,10)$
$b_{\text{s}}$	5.16	5.87	6.51	6.99	3.31	$(0.1,10)$
$a_{\text{fs}}$(kPa)	0.41	0.41	0.42	0.40	0.43	$(0.1,2)$
$b_{\text{fs}}$	11.3	11.52	11.09	12.05	10.28	$(0,20)$

Case 1: estimation from the proposed optimization procedure

Case 2: estimation using only the strain data in objective function

Case 3: estimation using only the first principal strain and volume data

Case 4: estimation terminated after the first step