Thermomechanics of Continua

Wilmanski, Krzysztof

doi:10.1007/978-3-642-58934-8

Cited by 104 publications

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“…We examine the underlying principles that hold at a solid-solid interface and we reformulate two different approaches to deriving the necessary conditions in the Lagrangian frame. The first approach [1] considers a solid to be a continuum; the second approach [2] views solids on atomistic scale. In reformulating each approach, we avoid assuming that either the transformation strain or the elastic strain is infinitesimal.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium conditions at a solid-solid interface

Plohr¹

2012

AIP Conference Proceedings

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Abstract. We derive the thermodynamic conditions necessary for two elasto-plastic solid phases to coexist in equilibrium. In doing so, we examine the well-known case of inviscid fluids and note the underlying physical principles so that we apply them to the case of solids. Beyond temperature, velocity, and traction continuity, these conditions require continuity of a generalization of the specific Gibbs free energy. We express this quantity in the Eulerian frame, as well as the Lagrangian frame. We also show that two approaches in deriving the equilibrium conditions, one on the continuum level and the other on the atomistic scale, yield the same results.

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Section: Introductionmentioning

confidence: 99%

Equilibrium conditions at a solid-solid interface

Plohr¹

2012

AIP Conference Proceedings

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“…From (3.5) and (3.7) we can then determine e In the one dimensional case an evolution equation for the infi ltration front X i (t) can be given: its velocity is a Lagrangian velocity, Wilmanski [36]; referring to Ambrosi [1] it can be written aṡ…”

Section: One Dimensional Problemmentioning

confidence: 99%

“…This means that the left solid border moves as a consequence of the relaxation of the matrix in the infi ltrated region. Referring to Gurtin [16] and Wilmanski [36], the Lagrangian framework is introduced on the solid constituent, in order to fi x the left solid border. Its position is indicated with X = 0.…”

Section: One Dimensional Problemmentioning

confidence: 99%

Infiltration condition and mouldability diagram in resin injection moulding

Mesin¹

2007

Comput. Appl. Math.

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Abstract. This paper deals with the modelling of injection moulding processes taking into account the deformability of the preform and the polymerisation of the resin. The coupled flow-deformation problem in the infi ltrated and dry region is formulated with the corresponding boundary conditions and with the proper evolution equations determining the motion of the boundaries. An approximated analytical discussion is performed to obtain some estimates on the infi ltration velocity, helping in identifying a window of applicability in the parameters space (i.e., the mouldability diagram), which fi ts well with the numerical simulations.Mathematical subject classification: 35K10, 35R35, 35L10.

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“…The field formulation or continuum thermodynamics deals with balance equations [Wilmanski (1988);Jou, Casas-Vazquez and Lebon (2001); Muschik, Papenfuss and Ehrentraut (2001)], which model together with the constitutive relations (equations of state) and the initial and boundary conditions of the process going on in the system. After having inserted the constitutive relations into the balance equations, we obtain a system of partial differential equations whose analytical solutions can be calculated only in sufficiently simple cases.…”

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confidence: 99%

Back Matter

2008

World Scientific Series on Nonlinear Science Series A

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Appendix A Thermodynamic interaction between two discrete systems in non-equilibrium 0 There are two different descriptions of thermodynamic systems: the field formulation and the description as a discrete (or lumped) system. The field formulation or continuum thermodynamics deals with balance equations [Wilmanski (1988);Jou, Casas-Vazquez and Lebon (2001); Muschik, Papenfuss and Ehrentraut (2001)], which model together with the constitutive relations (equations of state) and the initial and boundary conditions of the process going on in the system. After having inserted the constitutive relations into the balance equations, we obtain a system of partial differential equations whose analytical solutions can be calculated only in sufficiently simple cases. In numerous practical applications, these continuous models are replaced by approximations usually obtained by means of finite differences or finite elements. Calculations are carried out after having chosen an appropriate algorithm with respect to the problems of stability and convergence. Consequently for practical reasons it seems to be more convenient to have a direct description of the coupled thermodynamic behavior of a finite number of interacting elements or cells. This is just one of the reasons for introducing the concept of discrete systems [Muschik (1990)] because this gives a simple and effective possibility for describing thermodynamics and interactions of elements being in non-equilibrium. But here we encounter the analogous difficulties, which appears in classical thermodynamics, as noted by Truesdell and Bharatha [Truesdell and Bharatha (1977)] "the formal structure of classical thermodynamics describes the effects of changes undergone by 0 This Appendix represents results of the paper by W. Muschik and A. Berezovski (Thermodynamic interaction between two discrete systems in non-equilibrium. J. NonEquilib. Thermodyn., 29, (2004)

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Thermomechanics of Continua

Cited by 104 publications

References 0 publications

Equilibrium conditions at a solid-solid interface

Equilibrium conditions at a solid-solid interface

Infiltration condition and mouldability diagram in resin injection moulding

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