The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity

Coleman, Bernard D.; Noll, Walter

doi:10.1007/978-3-642-65817-4_9

Cited by 502 publications

(463 citation statements)

References 3 publications

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“…where S ∘ ext is the external entropy source, the rate of entropy exchange with the neighboring local systems per volume, and where S ∘ int is the internal entropy source, the rate of internal production of entropy (e.g., Coleman & Noll, 1963;Germain et al, 1983;Tolman & Fine, 1948;Truesdell, 1969). This internal source of entropy is the difference between the overall entropy production rate per volume,̇s, and S ∘ ext , which has two contributions: (1) r ext (2) a surface exchange term, the entropy flux, div…”

Section: Second Lawmentioning

confidence: 99%

A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

2018

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Microstructural evolution governs transient creep processes in the Earth at high temperature, on time scales from seconds to millions of years. Many experimental constraints and empirical models have been developed for discrete pieces of this problem, including flow laws and kinetic models for grain growth and dislocation recovery. We incorporate these models into a thermodynamic framework to develop a constitutive model for transient creep. The framework employed here is a branch of nonlinear thermodynamics of irreversible processes called the generalized standard materials formalism developed in solid mechanics over the last 40 years but minimally applied to geophysical problems. The generalized standard materials formalism is designed to incorporate a broad range of nonlinearity and coupling in the constitutive equations. To describe dynamic recrystallization, the model is constructed such that information propagates upward in length scale: [dislocation density → subgrain size → grain size], with each property evolving more slowly than the one below. We demonstrate that (1) the grain size‐stress piezometer may contain temperature dependence below a threshold in stress, (2) the microstructural evolution is strongly temperature dependent and thus dependent on thermal boundary conditions, and (3) the fraction of mechanical work done to the system that is diverted to changing the microstructure is not a constant but is at least a function of stress, temperature, dislocation density, and grain size. This kind of thermodynamically constrained analysis can be applied to torsional deformation experiments to extract further constraints on the subprocesses of microstructural evolution and transient creep.

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Section: Second Lawmentioning

confidence: 99%

A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

2018

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“…The formulations do not require any special material symmetry and hold for arbitrary body force distributions. The development, as provided here, describes how these boundary value problems follow as a matter of course from first principles of continuum mechanics and mixture theory as elaborated by Truesdell [5,7,15], Coleman & Noll [22], Bowen [1,2,6,30], and other workers during the heyday of rational mechanics.…”

Section: Discussionmentioning

confidence: 99%

“…In the non-equilibriuim setting -when there is relative motion between the liquid and solid constituents -there may be additional dissipative terms (say O s , O f and O b) added to the forms s , f and b as given earlier. These additional terms are subject to restrictions that trace back to a Coleman-Noll type development [22]. For example, in [8] these contributions are taken to be given by…”

Section: The Saturation Stress Concept Of Rajagopal and Winemanmentioning

confidence: 99%

On the formulation of boundary value problems with the incompressible constituents constraint in finite deformation poroelasticity

Pence

2012

Math Methods in App Sciences

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This paper considers the finite deformation theory of poroelasticity for the case in which a deformable solid constituent and an interpenetrating liquid constituent are each regarded as incompressible, and the mixing itself is regarded as taking place without the creation of voids. The resulting kinematical constraint gives rise to a Lagrange multiplier pressure in the resulting constitutive description. This pressure therefore enters into the separate momentum balance statements for each individual constituent. The formulation of boundary value problems in this context is well known in continuum mechanics. This paper examines how a systematic elimination of the Lagrange multiplier pressure from the mathematical formulation leads to a stress‐like tensor that generalizes a stress tensor concept introduced by Rajagopal and Wineman in the late 1980s, which they called the saturation stress. Here, by providing a rather complete development, it is discussed how boundary value problems are naturally formulated in terms of a single such stress tensor, how the constitutive theory is framed in terms of this stress tensor, and how certain questions concerning the formulation of boundary conditions are naturally addressed. Connections to the small deformation linear poroelastic (biphasic) theory are also provided. Copyright © 2012 John Wiley & Sons, Ltd.

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“…Substituting the rate of the Helmholtz free energy (Equation (11)) into the Clausius-Duhem inequality (Equation (10)) and making use of Equation (12) yield the following thermodynamic constraint [62,68]:…”

Section: Basic Thermodynamic Formulationsmentioning

confidence: 99%

“…The following thermodynamic conjugate forces and state laws can be defined by making use of Equation (13) [62,68]:…”

Section: Basic Thermodynamic Formulationsmentioning

confidence: 99%

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic, viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

Darabi

Al‐Rub

Masad

et al. 2011

Num Anal Meth Geomechanics

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SUMMARYBased on the continuum damage mechanics, a general and comprehensive thermodynamic-based framework for coupling the temperature-dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery-type nonlinear viscoelasticity, Perzyna-type viscoplasticity, and a viscodamage model analogous to the Perzyna-type viscoplasticity. The resulting constitutive equations are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep-recovery, creep, uniaxial constant strain rate, and repeated creep-recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.

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The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity

Cited by 502 publications

References 3 publications

A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

On the formulation of boundary value problems with the incompressible constituents constraint in finite deformation poroelasticity

Thermodynamic‐based model for coupling temperature‐dependent viscoelastic, viscoplastic, and viscodamage constitutive behavior of asphalt mixtures

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