Elimination of Pseudo Initial Stress for Proposed Invariants based Hyper elastic Strain Energy

Abstract

Although fitting of experimental data is important in selection of the best hyper elastic strain energy function, the zero stress condition in the initial (unstressed) configuration also should be taken into account. Therefore, in the current research a modification for an invariants based model was developed to eliminate the pseudo initial stress. To this goal, additional terms were added to hyper elastic strain energy as a function of the right Cauchy-Green deformation tensor. To justify the proposed algorithm, uniaxial loading of liver tissue and unfilled silicone rubber were studied via constitutive modeling in VUMAT user subroutine of ABAQUS software. Excellent agreement between the experimental and numerically predicted stress-stretch curves showed that the modified strain energy function enables to characterize the mechanical behavior of the liver tissue and unfilled silicone rubber. As the deformed shapes of soft tissues are important especially in the surgery operations, the effect of modification on the final deformed geometry was investigated. Results were shown the deformed profile of the modified and unmodified hyper elastic strain energy models were different.