The Use of Legendre Transformations in Developing the Constitutive Laws of Geomechanics from Thermodynamic Principles

Abstract

In recent years there has been much activity in the systematic development of theories of continua which start from the laws of thermodynamics. The books by Ziegler (1983), Lemaitre and Chaboche (1990) and Maugin (1992), and the articles by Germain, Nguyen and Suquet (1983) and Ziegler and Wehrli (1987) provide general accounts of these developments. Whilst these approaches provide a very elegant unified development of the theory of many of the model materials used in engineering including the so called “standard” elastic/plastic solids, they fail, in general, to include the type of elastic/plastic models commonly used to describe the behaviour of geomaterials — specifically materials which exhibit non-associated flow rules and which violate Drucker’s postulate. Building upon earlier work by Houlsby (1981, 1982) Collins and Houlsby (1996) have recently demonstrated that these “non-standard” models can be included in the general thermodynamic develpoment, provided the constitutive potentials and dissipation functions are suitably chosen — see also the paper by Houlsby (1996) in this volume.