A unified generalised invariants-based constitutive model for incompressible isotropic soft solids

A further generalisation in the constitutive theory of modelling the finite deformation of incompressible isotropic soft materials is presented in this work, on using the principal stretches . This generalisation seeks to achieve a constitutive model with a singular functional form for all applications to the large deformation of soft materials, replacing the expanding variety of 100+ strain energy functions currently in use in the literature. The construction of this unified model exploits a higher order response function in the generalised invariants, from the customary in Ogden-type models to a more general order
, and the use of the complete set of the generalised invariants. The ensuing model is of non-separable form in , and utilises the generalised invariants and in its functional form, with the latter appearing in the two-term expansion of the model. It is shown that: (i) the model parameters have physical relevance, (ii) the model is the parent to most existing classical strain energy functions, and (iii) provides accurate simulations of various challenging behaviours observed in the realm of the finite deformation of soft solids including strain hardening, soft elasticity, strain/shear softening, tension–compression asymmetry, anomalous inflation behaviour and instabilities, continuous softening (up to the onset of failure), and even post-yield plateau inter alia. This is demonstrated and verified by using extant experimental datasets on multiaxial deformation of a wide range of materials, spanning across classical unfilled and filled vulcanised rubbers, biomaterials, hydrogels, liquid crystal elastomers and thermoplastic polymers etc. The presented strain energy function in this work offers an explicit step forward towards the elusive universal model.