Hello,

I am trying to resolve a discrepancy I have noticed in the governing equations behind Abaqus. For context, I am attempting to fit the Mooney-Rivlin coefficients of a hyperelastic material using data from a uniaxial tensile test, and then use these coefficients to define the material in Abaqus. The Mooney-Rivlin equation says strain energy density U = C_10*(I_1 - 3) + C_01*(I_2 - 3) with C_01 and C_10 being unknowns.

I am using an external program to fit the coefficients, so I would like to derive the actual Abaqus equation for uniaxial tensile stress and ensure it is the same as my definition. This is done using the definition provided in the documentation (Uniaxial tensile test section in https://abaqus-docs.mit.edu/2017/English/SIMACAEMATRefMap/simamat-c-hyperelastic.htm#simamat-c-hyperelastic-t-ExperimentalTests-sma-topic24).

According to my calculations provided in the attached image, the engineering stress-strain equation should be T_U = 4*C_10*(λ_1−λ_1^−2)+4*C_01*(1−λ1^−3). However, Abaqus seems to treat the equation as T_U = 2*C_10*(λ_1−λ_1^−2)+2*C_01*(1−λ1^−3), off by a factor of 2.

I have shown this by fitting my coefficients and plotting in Excel (using the equation T_U = 4*C_10*(λ_1−λ_1^−2)+4*C_01*(1−λ1^−3)), then comparing to the stress-strain plot generated when I evaluate the material in Abaqus (see 2 attached images). You can see that the magnitude of all stress values in the Excel plot is double that of the stress values at equivalent strains in the Abaqus plot.

Is anyone here intimately familiar with how Abaqus defines the Mooney-Rivlin equation for uniaxial tensile tests? I would like to reconcile this discrepancy.