Application of thermomechanical principles to the modelling of geotechnical materials

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.

[1]  M. J. Sewell Legendre Transformations and Extremum Principles , 1982 .

[2]  M. J. Sewell,et al.  Maximum and minimum principles , 1989, The Mathematical Gazette.

[3]  Chandrakant S. Desai,et al.  Induced anisotropy during plastic straining , 1984 .

[4]  元 松岡,et al.  “Stress-Deformation and Strength Characteristics of Soil under Three Different Principal Stresses” への討議 , 1976 .

[5]  P. Lade,et al.  SINGLE HARDENING CONSTITUTIVE MODEL FOR FUNCTIONAL MATERIALS. 1: PLASTIC POTENTIAL FUNCTION , 1988 .

[6]  H. Chandler Homogeneous and localised deformation in granular materials: A mechanistic model , 1990 .

[7]  Lyesse Laloui,et al.  Thermodynamical approach for CamClay‐family models with Roscoe‐type dilatancy rules , 1994 .

[8]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[9]  B. Reddy,et al.  Internal Variable Formulations of Problems in Elastoplasticity: Constitutive and Algorithmic Aspects , 1994 .

[10]  P. Stutz,et al.  On formulation of stress-strain relations for soils at failure , 1968 .

[11]  H. Chandler A variational principle for granular materials , 1988 .

[12]  H. Ziegler Discussion of some objections to thermomechanical orthogonality , 1981 .

[13]  T. Y. Thomas INTERDEPENDENCE OF THE YIELD CONDITION AND THE STRESS-STRAIN RELATIONS FOR PLASTIC FLOW. , 1954, Proceedings of the National Academy of Sciences of the United States of America.

[14]  B. Reddy,et al.  Piecewise smooth dissipation and yield functions in plasticity , 1993 .

[15]  Rodney Hill,et al.  Elastic potentials and the structure of inelastic constitutive laws , 1973 .

[16]  H. Ziegler Non-linearity in thermomechanics , 1975 .

[17]  J. Lubliner On the thermodynamic foundations of non-linear solid mechanics , 1972 .

[18]  Poul V. Lade,et al.  Single hardening constitutive model for frictional materials , 1988 .

[19]  D. Wood Soil Behaviour and Critical State Soil Mechanics , 1991 .

[20]  Rodney Hill,et al.  Some basic principles in the mechanics of solids without a natural time , 1959 .

[21]  B. D. Reddy,et al.  An internal variable theory of elastoplasticity based on the maximum plastic work inequality , 1990 .

[22]  Quoc Son Nguyen,et al.  Sur les matériaux standard généralisés , 1975 .

[23]  P. M. Naghdi,et al.  On continuum thermodynamics , 1972 .

[24]  G. Houlsby The work input to a granular material , 1979 .

[25]  J. Rice Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[26]  J. Moreau,et al.  Sur les lois de frottement, de plasticité et de viscosité , 1970 .

[27]  R. Hill Constitutive dual potentials in classical plasticity , 1987 .

[28]  J. Rice,et al.  PARADOXES IN THE APPLICATION OF THERMODYNAMICS TO STRAINED SOLIDS. , 1969 .

[29]  H. W. Chandler,et al.  A plasticity theory without drucker's postulate, suitable for granular materials , 1985 .

[30]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[31]  Rodney Hill,et al.  Aspects of Invariance in Solid Mechanics , 1979 .

[32]  Christoph Wehrli,et al.  The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function , 1987 .

[33]  Guy T. Houlsby,et al.  A study of plasticity theories and their applicability to soils , 1981 .

[34]  R. Butterfield,et al.  A NATURAL COMPRESSION LAW FOR SOILS (AN ADVANCE ON E-LOG P') , 1979 .

[35]  G. Houlsby Interpretation of Dilation as a Kinematic Constraint , 1993 .