Continuous softening as a state of hyperelasticity: Examples of application to the softening behaviour of the brain tissue

The continuous softening behaviour of the brain tissue, i.e., the softening in the primary loading path with increase in deformation, is modelled in this work as a state of hyperelasticity, up to the onset of failure. That is, the softening behaviour is captured via a core hyperleastic model, without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behaviour. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behaviour of the tissue, by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviours of the specimens favourably, and also predicts the behaviour at other rates. These results offer a clear set of advantages in favour of the considered modelling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behaviour, over the existing models in the literature which at best may purport to capture only a reduced set of the foregoing behaviours, and with ill-posed effects.