Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Abstract A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types rubber-like materials; (ii) describes constitutive subject specimen under different deformation modes via single set parameter values, and (iii) is parent to many existing models distinct types, presented in this paper for application finite incompressible isotropic materials. The breaks away from Rivlin’s principal invariants $I_{i}$ I i Valanis-Landel’s separable function stretches $\lambda _{i}$ ? representations, instead adopts general non-separable functional form $W( \lambda _{1}, _{2}, _{3} )$ W ( 1 , 2 3 ) , incompressibility constraint. By way example, extant datasets four materials that exhibit discernible behaviours, namely natural unfilled filled rubbers, hydrogels (extremely) soft tissue specimens, will be considered. favourable correlation between predictions considered experimental datasets, obtained simultaneous fitting data deformations, demonstrated. It shown most landmark literature including I_{1}, I_{2} Mooney-Rivlin, Gent-like limiting chain extensibility, nonaffine tube stretches-based type Ogden are all special sub-set recovered model. An important implication conferred, through specific dataset, where functions prove inherently inadequate. consequences these improvements more accurate modelling also discussed.