A unified pseudo-elastic model of continuous and discontinuous softening in the finite deformation of isotropic soft solids

Building on a recently devised approach of hyperelasticity with intrinsic softening, a new framework for capturing both continuous and discontinuous softening in the finite deformation of isotropic incompressible elastomers is considered here. The continuous and discontinuous softening effects of interest pertain to the loading and unloading paths, respectively, and the model is developed within the theory of pseudo-elasticity. The performance of the model in capturing these effects is then compared with the deformation behaviour of a variety of elastomers, including a range of hydrogels from truly independent double-network (t-DN) to tough and nanocomposite hydrogels, dielectric elastomers and carbon-black filled rubber specimens, under uniaxial and multiaxial deformations. The model is demonstrated to show a favourable simulation and prediction of the extant experimental data. The application of the model is then extended to capturing the softening behaviour under rate-dependent loading, based on a prior work by the authors incorporating the rate effects directly into the pseudo-hyperelastic model, by assuming that the model parameters evolve with the deformation rate. The capability of the model to capture the rate-dependent effects accurately will be shown by considering the rate-dependent behaviour of two hydrogel specimens. Given the simplicity of the functional form of the model, akin to a standard pseudo-elastic model, the low(er) number of model parameters, the ability to capturing the softening behaviour in the deformation of a wide range of elastomeric materials, and the easy extension for incorporating additional features such as the rate-effects, the proposed model provides another step towards the unification of various complex deformation features into a single modelling framework, for a more universal application to the finite deformation of soft solids.