Review on Thermo-mechanical Approach in the Modelling of Geo-materials Incorporating Non-associated Flow Rules

Recently, there has been a burgeoning interest in developing constitutive soil models from the laws of thermodynamics, mainly due to the benefits that these models automatically obey them and the approach provides a well-established structure and reduces the need for ‘ad hoc’ postulates. A thermodynamic framework, also known as thermo-mechanical framework, has the capability to predict the behaviour of geotechnical materials, which requires the anticipated incorporation of non-associated flow rules. As it is very challenging to achieve acceptable accuracy in plasticity modelling of granular materials, this paper aims to review this framework not only to discuss the details of the major components but also to highlight the capability of generating non-associated flow rules in a natural way from thermo-mechanical principles. This approach introduces the use of internal variables to develop the two thermodynamic potentials (the free energy and the rate of dissipation functions), sufficient to derive the corresponding yield function, flow rule, isotropic and kinematic hardening rules as well as the basic elasticity law. It is shown that the non-associated flow rule can be derived naturally from the postulated stress-dependent dissipation increment function. Comparison has been made with stress-independent dissipation to demonstrate that the approach can also successfully explain the behaviour of standard materials with associated flow rules. The basic steps for the thermo-mechanical formulation for developing a constitutive model are also reviewed and summarised. Furthermore, the power of conventional mathematical technique, Legendre transformation, in the derivation of constitutive equations has been highlighted.