Constitutive Coefficients for Viscohyperelastic Materials

Abstract : Elastic and viscous stresses in rubberlike materials can be modeled using strain energy density functions. The large strain elastic (hyperelastic) deformations are often modeled with the Rivlin strain invariant power series 1 . Similarly, large strain viscous deformations of rubberlike materials (viscohyperelastic) can be modeled using an internal solid theory with hyperelastic solids 2,3,4,5. The energy function's material coefficients are found by least square fitting to the classical tension, shear, and equibiaxial stress-stretch tests 6. These least squares fits typically produce energy functions which are not stable for deformations other than those covered by the test data. That is, when strain states not included in the test data are considered the models often suffer from the flaw that (for isothermal deformations) they predict a decrease in the solid's internal strain energy for an increment of applied stress which does positive work on the solid. This conservation of energy statement is known as Drucker's postulate on stability. Such a flaw cannot be accepted since computations for complex deformations will include strain states which are not the same as those used to determine the energy density function.