TY - JOUR

T1 - A thermo-mechanical continuum theory with internal length for cohesionless granular materials

T2 - PPart I. A class of constitutive models

AU - Fang, Chung

AU - Wang, Yongqi

AU - Hutter, Kolumban

PY - 2006/7/1

Y1 - 2006/7/1

N2 - A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory [1-3]; it is constructed by removing these inconsistencies through the introduction of an internal length l. Four constitutive models are proposed and discussed in which l is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.

AB - A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory [1-3]; it is constructed by removing these inconsistencies through the introduction of an internal length l. Four constitutive models are proposed and discussed in which l is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.

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U2 - 10.1007/s00161-006-0007-8

DO - 10.1007/s00161-006-0007-8

M3 - Article

AN - SCOPUS:33745666855

VL - 17

SP - 545

EP - 576

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 8

ER -