A Comparison between the Exponential and Limiting Fiber Extensibility Pseudo-elastic Model for the Mullins Effect in Arterial Tissue

This study compares the capability of two different mathematical forms of the so-called softening variable to describe strain-induced stress softening observed within cyclic uniaxial tension of the human thoracic aorta. Specifically, the softening variable, which serves as the stress reduction factor, was considered to be tangent hyperbolic-based and error function-based. The mechanical response of the aorta was assumed to be pseudo-hyperelastic, incompressible and anisotropic. The strain energy density function was employed in a classical exponential form and in a not well-known limiting fiber extensibility model. This study revealed that both the limiting fiber extensibility and exponential models of the strain energy describe mechanical the response of the material with similar results. It was found that it is not a matter which kind of the softening variable is employed. It was concluded that such an approach can fit the Mullins effect in the human aorta, however the question of the best fitting model still remains.