A constitutive framework for modelling elastomers, soft tissues and liquid crystal elastomers

Source abstract

This manuscript presents a constitutive modelling framework designed to characterize a wide range of soft materials. The framework uses an exponential-power law to develop a six-parameter generic hyperelastic potential function, while a two-parameter viscous dissipation function is formulated to address strain-rate sensitive materials. Independent validations of the hyperelastic and visco-hyperelastic components are carried out to rigorously evaluate the model’s performance. The hyperelastic component is validated in two ways: (i) through a reduced three-parameter model, specifically suited for soft elastomers exhibiting a simple S-shaped stress–strain response and (ii) through the six-parameter generic model, which accommodates more complex datasets exhibiting non-S-shaped stress–strain behaviour. The reduced three-parameter model effectively captures the mechanical behaviour of soft elastomers, while the six-parameter hyperelastic framework describes the intricate mechanical responses of complex materials, such as soft elastomers with non-S-shaped responses, human brain tissue, porcine liver tissue and liquid crystal elastomers (LCEs). Apart from hyperelastic fitting the viscoelastic component is validated using strain-rate sensitive soft-tissue data where the two-parameter viscous dissipation function accurately models the strain-rate sensitive behaviour of soft tissues.