Application of thermomechanical principles to the modelling of geotechnical materials

Abstract

A thermodynamic framework is presented for the plasticity modelling of geotechnical materials. The framework is capable of modelling rigorously both friction and non-associated flow, and the strong connection between these phenomena is demonstrated. The formulation concentrates on the development of constitutive models from hypotheses about the form of an energy potential and a dissipation function. The reformulation of previous work, in which the Helmholtz free energy was used, to a new approach starting from the Gibbs free energy is found to be valuable. The relationship between the new functions and classical plasticity concepts (yield surface, plastic potential, isotropic and kinematic hardening, friction, dilation) is demonstrated. Comments are made on elastic-plastic coupling. Implications of the new approach for critical state soil models are discussed.

Potentials for the modified Cam-Clay model

“…in the first part of this section, the assumptions of Collins and Houlsby (1997) and Houlsby and Puzrin (2006).…”

“…An alternative choice may be the pair (ε, ε p , β) and (σ, κ, A) as adopted, for instance, in Collins and Houlsby (1997).…”

“…G. T. Houlsby and coworkers (Collins and Houlsby, 1997;Houlsby and Puzrin, 2006) contributed with the concept of Hyperplasticity, which is a complete methodology to consistently develop constitutive equations based on thermodynamic principles. Rich and rigorous contributions to thermomechanics with internal variables are also found in Maugin (1992), Han andReddy (1999) andŠilhavý (1997).…”

A unique Critical State two-surface hyperplasticity model for fine-grained particulate media

“…As discussed by Collins and Houlsby (1997), the plastic strain increment is given by a normal flow rule in dissipative stress space. This only implies an associated model in true stress space under the condition that the dissipation rate is independent of the true stress, σ ij 5 .…”

Constitutive behaviour of quasi-brittle materials with anisotropic friction

“…Recently the theoretical and numerical problems about the variational formulation of nonassociated law has been developed (Collins and Houlsby, 1997), although the complexity of the problem welcomes more studies in the future.…”