Characterization of nonlinear elastic properties of beef products under large deformation
Knowledge of mechanical properties of beef is important for studying its tenderness and improving tenderness 
measurement techniques. This research was initiated to develop a three-dimensional constitutive equation to describe the 
nonlinear stress-strain relationship of beef products in large deformations, to determine the constitutive parameters, and 
to validate the model for multidimensional stress/strain states. Based on experimental observations and the theory of finite 
elasticity, a three-dimensional constitutive equation was proposed, which assumes that the materials are isotropic and 
incompressible. Uniaxial compression tests were performed on twenty samples each of bologna, salami, and smoked 
sausage to determine the two parameters in the constitutive equation. Confined two-dimensional compression tests were 
also conducted to validate the constitutive equation. Experimental results showed that beef products exhibited a 
pronounced nonlinearity under uniaxial compression; the slope of the force-deformation curves increased monotonically 
with the increasing deformation. The constitutive equation fitted the stress-strain curves well for the three products. The 
constitutive equation predicted well the stress-strain responses of the beef products under confined two-dimensional 
loading; the differences between predicted and measured values were mostly not significant at the 0.05 level. This 
constitutive equation can be used to predict stress-strain responses of beef products under different loading conditions.