On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

Hütter, Markus; Svendsen, Bob

doi:10.1007/978-94-007-1884-5_23

Cited by 10 publications

(18 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is formally analogous to the case of the viscosity tensor in a GENERIC-based formulation of a model for thermoelastic solids with heat conduction and viscosity (see e.g., [23]). On this basis, the symmetry condition (41) 3 is satisfied identically.…”

Section: Friction Operator and Irreversible Partmentioning

confidence: 93%

“…This represents a direct generalization of the choice x = (χ , m, θ ) made in [23] for the case of thermoelasticity with heat conduction and viscosity to the current case. Note that this choice is not unique.…”

Section: Choice Of Variablesmentioning

confidence: 95%

“…Since attention is restricted in this work to local material behavior for simplicity, it suffices to work with a form of the GENERIC based on local (i.e., differential) operators. In addition, as implied by the case of thermoelasticity with heat conduction and viscosity [23], it is useful for the case of solids to work with a representation of the GENERIC in terms of the densities e and η, respectively, of the total energy E and total entropy S, respectively. On this basis, the form of the GENERIC utilized in this work is given byẋ…”

Section: Form Of the Generic Used In This Workmentioning

confidence: 99%

“…Originally developed for complex fluids, the GENERIC-based approach has recently been used [21,22] to formulate GENERIC-based models for anisotropic elastic and elastoplastic solids in a Eulerian setting. An alternative approach to the formulation of GENERIC-based models for inelastic solids was pursued in [23], who examined the case of thermoelastic solids with heat conduction and viscosity in a Lagrangian setting. Recently, a GENERIC-based formulation of models for inelastic materials (e.g., viscoelastic, elastoplastic) has been discussed in [24].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a GENERIC-based formulation of models for inelastic materials (e.g., viscoelastic, elastoplastic) has been discussed in [24]. The purpose of the current work is to apply the approach of [23] to the formulation of a GENERIC-based model for thermoelastic, viscoplastic solids (which we understand to include heat conduction). In particular, this is based on a GENERIC-based form for the viscoplastic flow rule.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Hütter

Svendsen

2012

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

Thermodynamic models for viscoplastic solids are often formulated in the context of continuum thermodynamics and the dissipation principle. The purpose of the current work is to show that models for such material behavior can also be formulated in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC), see, e.g., Grmela and Öttinger (Phys Rev E, 56:6620-6632, 1997), Öttinger and Grmela (Phys Rev E, 56:6633-6655, 1997), Grmela (J Non-Newtonian Fluid Mech, 165:980-986, 2010). A GENERIC combines Hamiltonian-dynamics-based modeling of time-reversible processes with Onsager-Casimir-based modeling of time-irreversible processes. The result is a model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to model complex fluids, it has recently been applied to anisotropic inelastic solids in Eulerian (Hütter and Tervoort, in J Non-Newtonian Fluid Mech, 152:45-52, 2008; Hütter and Tervoort, in J Non-Newtonian Fluid Mech, 152:53-65, 2008; Hütter and Tervoort, in Adv Appl Mech, 42:254-317, 2008) and Lagrangian (Hütter and Svendsen, in J Elast 104:357-368, 2011) settings, as well as to damage mechanics. For simplicity, attention is focused in the current work on the case of thermoelastic viscoplasticity. Central to this formulation is a GENERIC-based form for the viscoplastic flow rule. A detailed comparison with the formulation based on continuum thermodynamics and the dissipation principle is given.

show abstract

Section: Friction Operator and Irreversible Partmentioning

confidence: 93%

Section: Choice Of Variablesmentioning

confidence: 95%

Section: Form Of the Generic Used In This Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Hütter

Svendsen

2012

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

show abstract

An energy momentum consistent integration scheme using a polyconvexity‐based framework for nonlinear thermo‐elastodynamics

Franke

Janz

Schiebl

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

The present contribution provides a new approach to the design of energy momentum consistent integration schemes in the field of nonlinear thermo-elastodynamics. The method is inspired by the structure of polyconvex energy density functions and benefits from a tensor cross product that greatly simplifies the algebra. Furthermore, a temperature-based weak form is used, which facilitates the design of a structure-preserving time-stepping scheme for coupled thermoelastic problems. This approach is motivated by the general equation for nonequilibrium reversible-irreversible coupling (GENERIC) framework for open systems. In contrast to complex projection-based discrete derivatives, a new form of an algorithmic stress formula is proposed. The spatial discretization relies on finite element interpolations for the displacements and the temperature. The superior performance of the proposed formulation is shown within representative quasi-static and fully transient numerical examples. KEYWORDSfinite element method, nonlinear thermo-elastodynamics, polyconvexity-based framework, structure-preserving discretization, tensor cross product INTRODUCTIONThe present contribution aims for the consistent discretization of nonlinear thermo-elastodynamics. The emphasis of this paper is on both theoretical and numerical aspects. In recent decades, thermomechanical constitutive models have been addressed in numerous works (see, eg, the works of Miehe, 1 Holzapfel and Simo, 2 and Reese and Govindjee 3 as well as textbooks by Holzapfel 4 and Gonzalez and Stuart 5 ). Classically, the hyperelastic Helmholtz free-energy density function depends only on the deformation gradient and the temperature. Furthermore, the weak form is deduced from its strong form. Dependent on the chosen material model, eg, for a Mooney-Rivlin model, the consistent linearization may lead to cumbersome expressions. In contrast to the classic approach, the present work is inspired by the concept of polyconvexity (see, eg, the works of Ball 6 and Ciarlet 7 ), where the Helmholtz free energy is a convex function of the deformation gradient, its cofactor, and its determinant and is concave with respect to absolute temperature. In addition to the polyconvexity-based framework, the present work relies on the cross product between second-order tensors, as introduced in the work of de Boer 8 (see also Appendix B 4.9.3 in another work of de Boer 9 ). This tensor cross product has been used in the context of large-strain Int J Numer Methods Eng. 2018;115:549-577. wileyonlinelibrary.com/journal/nme 549 550 FRANKE ET AL.hyperelasticity in the works of Bonet et al 10,11 and remarkably simplifies the algebraic manipulation of the large-strain continuum formulation and is extended herein to the thermomechanical formulation. Furthermore, the polyconvexity-based framework makes possible a wide range of advanced finite element technologies in the context of continuum mechanics. For example, the introduction of mixed finite elements, 10,12 phase-field fracture models, 13 anisotropic...

show abstract

Energy‐momentum‐entropy consistent numerical methods for large‐strain thermoelasticity relying on the GENERIC formalism

Betsch

Schiebl

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary In the present paper, structure‐preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the general equation for nonequilibrium reversible‐irreversible coupling (GENERIC) formalism and makes possible the free choice of the thermodynamic state variable. The notion “GENERIC consistent space discretization” is introduced, which facilitates the design of Energy‐Momentum‐Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. Numerical examples confirm the structure‐preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.

show abstract

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

Cited by 10 publications

References 21 publications

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

Thermodynamic model formulation for viscoplastic solids as general equations for non-equilibrium reversible–irreversible coupling

An energy momentum consistent integration scheme using a polyconvexity‐based framework for nonlinear thermo‐elastodynamics

Energy‐momentum‐entropy consistent numerical methods for large‐strain thermoelasticity relying on the GENERIC formalism

Contact Info

Product

Resources

About