Bounded Multi-axial Elastic Potentials With Strain-stiffening Effects For Rubbery Materials Based On Uniaxial Data

Rubberlike materials are widely used in engineering and our daily life due to their unique properties such as large recoverable elastic deformation, etc. The study of the large deformation elastic behavior or accurate characterization of the stress-strain relationship is of much importance in engineering. According to thermodynamic principles, the relationship between the stress and strain of an elastomer is determined by the elastic potential, Because of large deformations and the effect strain-stiffening effect, determination of the multi-axial elastic potential for rubberlike materials not only needs to deal with strong geometrical and physical nonlinearities, but also needs to cope with the strain-stiffening complexity associated with sharply increasing stresses at certain strain limits.Based on most recent advances in modeling incompressible, isotropic hyper-elastic rubberlike materials, we develop a direct, explicit method of constructing strain-energy functions with strain-stiffening effects. The multi-axial potentials are derived directly from one-dimensional stress-strain relationship for the uniaxial case by means of explicit procedures. As such, usual tedious numerical calculations in estimating a set of unknown parameters may be bypassed. New results are presented for the purpose of meeting the following three requirements:(1) the strain-stiffening is represented with rapidly growing stresses at certain strain limits,(2) the strain energy never grows to infinity but is always bounded, and(3) the stress is also bounded and asymptotically tends to vanish with increasing strain up to failure.It is shown that the proposed potentials based solely on uniaxial data can meet the three requirements above and accurately match data of four benchmark tests over the whole stretch range from small to large deformations and, in particular, can for the first time present a direct simulation of the material behavior over the entire deformation range up to failure.