Table 1.

Summary of all problems considered, indicating force-controlled (FC) and displacement-controlled (DC) cases

Problem	Model	Input	Output	Type
1D curve fitting	(1)	Strain $\mathit{ϵ}$	Stress $\mathit{\sigma }$	DC
	(3)	Strain $\mathit{ϵ}$	Stress $\mathit{\sigma }$	DC
	(5)	Strain $\mathit{ϵ}$	Stress $\mathit{\sigma }$	DC
	(6)	Strain $\mathit{ϵ}$	Stress $\mathit{\sigma }$	DC
	(2)	Stress $\mathit{\sigma }$	Strain $\mathit{ϵ}$	FC
	(4)	Stress $\mathit{\sigma }$	Strain $\mathit{ϵ}$	FC
Multi-D curve fitting	(9)	Deformation gradient $\mathbf{F}$	$2\text{nd}$ PK Stress $\mathbf{S}$	DC
	(7)	Deformation gradient $\mathbf{F}$	$2\text{nd}$ PK Stress $\mathbf{S}$	DC
Inverse modeling of biaxial setup	SM (9)	Displacement boundary conditions	Edge forces	DC
	GOH (7)	Displacement boundary conditions	Edge forces	DC
	SM (9)	Force on edges	Edge deformation	FC
	GOH (7)	Force on edges	Edge deformation	FC
Inverse modeling of shape matching	SM (9)	Pressure	Deformed shape	FC
	GOH (7)	Pressure	Deformed shape	FC