The thermodynamics of elastic materials with heat conduction and viscosity

Coleman, Bernard D.; Noll, Walter

doi:10.1007/bf01262690

Cited by 1,744 publications

(634 citation statements)

References 4 publications

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“…Therefore, we take the view that within the phase-field setting Equation (2.9) has the same fundamental physical priority as Equations (2.1)-(2.8). A second rationale for postulating the micro-forces is that in the presence of other dissipative mechanisms like conductive heat transfer or the diffusion of species within the material, the micro-force balance can be applied within the second law of thermodynamics using the systematic approach established by Coleman and Noll (1963) to determine the constraints on the constitutive dependencies.…”

Section: Discussionmentioning

confidence: 99%

“…The answer being that since the internal micro-force π i is allowed to depend on i P , then all of the thermodynamic forces must also potentially have such dependence (Coleman and Noll, 1963). It will be shown that the second law inequality ultimately allows only π i to depend on i P (see Equations (2.13) and (2.14)).…”

Section: Theorymentioning

confidence: 99%

“…It will be shown that the second law inequality ultimately allows only π i to depend on i P (see Equations (2.13) and (2.14)). Following Coleman and Noll (1963) …”

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Landis

2007

Journal of the Mechanics and Physics of Solids

267

207

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Section: Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

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Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Landis

2007

Journal of the Mechanics and Physics of Solids

267

207

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“…The expression for the driving force for transformation is derived from the procedure of Coleman and Noll [31] that requires a formulation of the energy dissipation and subsequent application of the second law of thermodynamics. Through this procedure the rate of change in the martensitic volume fractionξ (α) is identified as a flux and the driving force f (α) as the corresponding affinity.…”

Section: Transformation Driving Forcementioning

confidence: 99%

Modelling of the effects of grain orientation on transformation-induced plasticity in multiphase carbon steels

Tjahjanto

Turteltaub

Suiker

et al. 2006

Modelling Simul. Mater. Sci. Eng.

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The effects of grain orientation on transformation-induced plasticity in multiphase steels are studied through three-dimensional finite element simulations. The boundary value problems analysed concern a uniaxiallyloaded sample consisting of a grain of retained austenite surrounded by multiple grains of ferrite. For the ferritic phase, a rate-dependent crystal plasticity model is used that describes the elasto-plastic behaviour of body-centred cubic crystalline structures under large deformations. In this model, the criticalresolved shear stress for plastic slip consists of an evolving slip resistance and a stress-dependent term that corresponds to the projection of the stress tensor on a non-glide plane (i.e. a non-Schmid stress). For the austenitic phase, the transformation model developed by Turteltaub and Suiker (2006 Int. J. Solids Struct. at press, 2005 J. Mech. Phys. Solids 53 1747 is employed. This model simulates the displacive phase transformation of a face-centred cubic austenite into a body-centred tetragonal martensite under external mechanical loading. The effective transformation kinematics and the effective anisotropic elastic stiffness components in the model are derived from lower-scale information that follows from the crystallographic theory of martensitic transformations. In the boundary value problems studied, the mutual interaction between the transforming austenitic grain and the plastically deforming ferritic matrix is computed for several grain orientations. From the simulation results, specific combinations of austenitic and ferritic crystalline orientations are identified that either increase or decrease the effective strength of the material. This information is useful to further improve the mechanical properties of multiphase carbon steels. In order to quantify the anisotropic 1 Author to whom any correspondence should be addressed.

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“…The spatial position in the deformed configuration is denoted by x = χ (X, t), where X ∈ Ω 0 , and the deformation gradient is defined by F = ∂x/∂X [29].…”

Section: Thermodynamic Frameworkmentioning

confidence: 99%

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

Haldar

Lagoudas

2014

Proc. R. Soc. A.

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A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.

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The thermodynamics of elastic materials with heat conduction and viscosity

Cited by 1,744 publications

References 4 publications

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

Modelling of the effects of grain orientation on transformation-induced plasticity in multiphase carbon steels

Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries

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