A new 3D finite element for the finite deformation of nearly incompressible hyperelastic solids

Volumetric locking is exhibited by nearly incompressible solids such as rubber, resulting in over-stiffening response of the finite element mesh. In this work, we developed the displacement-based computationally efficient volumetric locking-free 3D finite element using smoothening of determinant of deformation gradient (J-Bar method) within the framework of isotropic hyperelasticity. The developed methodology is employed to analyse a rubber block undergoing finite stretch and bending deformations. The convergence study for finite stretch and bending of rubber block is presented. Results of the analysis show that J-Bar method efficiently removes the volumetric locking.