The difficult challenge of modelling the non‐linear elastic behaviour of soils within a theoretically sound framework

Hypo‐elastic relations are often adopted to simulate the recoverable non‐linear behaviour of soils within elasto‐plastic constitutive models. In reality, they are unable to reproduce the elastic, ie, recoverable, response of materials; hence, they introduce severe inconsistencies in models based on the decomposition of the total strain tensor into its recoverable and permanent parts. Hyper‐elasticity should then be used. However, existing models developed within this framework do not satisfy a number of fundamental theoretical requirements. A new hyper‐elastic model is proposed, which is rigourously formulated by integrating some of the main relations which emerge from experimental results. The model satisfies all theoretical requirements and also possesses features that are fundamental for its numerical integration. The model can be considered as the correct hyper‐elastic version of the classical hypo‐elastic constitutive relation adopted in models based on the Critical State framework, such as the Modified Cam‐Clay, with a constant Poisson's ratio.