Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters

Čanađija, Marko; Brnić, Josip

doi:10.1016/j.ijplas.2003.11.016

Cited by 50 publications

(34 citation statements)

References 33 publications

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“…In other works, e.g. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], the problems regarding large thermal and elasto-plastic deformations were considered, appropriate measures to be applied for deformations, additivity of elastic and plastic deformations were established, and problems regarding actual and relative configurations were described. The topics of linear and nonlinear kinematic and isotropic hardening were analysed in papers [30,35,39].…”

Section: Zśloderbach (B)mentioning

confidence: 99%

“…In addition, problems regarding the stability and behaviour under thermomechanical and mechanical loading were analysed, see e.g. [24,25,27,31,33,40,44]. The majority of papers describing large deformations in thermo-elasto-plasticity apply the method of internal parameters in the frame of thermodynamics of non-reversible processes, for example see [13,14,21,22,26,28,31,33,36,43,44 …”

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Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

Śloderbach

2016

Continuum Mech. Thermodyn.

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This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337-349, 351-367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.Keywords Bifurcation of the equilibrium state · Conditions and criteria of uniqueness · Boundary-value problem · Generalized coupled thermo-elasto-plasticity · Comparison bodies IntroductionThe incremental boundary-value problem of generalized coupled thermoplasticity is formulated in this paper. This is followed by an interpretation of the uniqueness conditions for the solution of that problem. The necessary and sufficient local uniqueness conditions are deduced together with the global sufficient uniqueness condition. A similar incremental boundary-value problem of coupled generalized thermoplasticity was investigated and discussed [1,3]. In this paper, necessary and sufficient local and global conditions of uniqueness of solution of an incremental boundary-value problem of coupled generalized thermoplasticity for the case of small displacements gradients (small strains) are derived. Uniqueness conditions for the generalized coupled thermoplasticity [1][2][3] and suitable comparison bodies [1][2][3][4][5][6][7] are identified for this purpose. The derived local and global uniqueness conditions are suitable necessary and sufficient conditions excluding occurrence of the bifurcation of equilibrium state in coupled generalized thermoplasticity and for suitable comparison bodies (also in isothermal loading processes).Early papers by Mróz [8,9] defined local conditions of uniqueness for solving an incremental boundary problem for the case of non-associated laws of plastic flow, for isothermal processes and small strains. A similar local condition was obtained by Hueckel and Maier in [10,11]. In their analysis, the stability of the material is defined by means of a condition which states that the half of the product of the stress rate tensor needs to be a positive value. The reported study was confined to the case of the isothermal theory of plasticity (with Communicated by Andreas Öchsner. Z.Śloderbach (B)Faculty of Applications of Chemistry and Mechani...

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Section: Zśloderbach (B)mentioning

confidence: 99%

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confidence: 99%

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

Śloderbach

2016

Continuum Mech. Thermodyn.

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“…Armero and Simo J.C. [10]; Benall and Bigoni, [11]; Bertram, [12]; Candija and Brnic, [13]; Casey, [14]; Epstein and Maugin, [15]; Hakansson et al, [16]; Huttel and Matzenmiller, [17]; Itskov, [18]; Lehmann, [19]; Mahnken and Stein, [20]; Marakin and Sokolova, [21]; Maugin and Epstein,, [22]; Meyers et al, [23]; Miehe, [24]; Srinivasa, [25]; Xiao et al [26]; Nguyen, [27]; Śloderbach and Pajak, [28], [29]; Śloderbach, [7], [8], [30]). The constitutive equations and plasticity conditions for isotropic and anisotropic materials were analyzed in these papers; the methods of numerical calculations were also used.…”

Section: Introductionmentioning

confidence: 99%

“…In some works, (e.g. Bertram, [12]; Candija and Brnic, [13] [26]) the problems of description of large thermo and elasto-plastic deformations and taking appropriate measures for deformations, additivity of elastic and plastic deformations and problems related to actual and relative configurations were considered. In papers (Mahnken and Stein, [20]; Meyers et al, [23]) the topics of linear and non-linear kinematic and isotropic reinforcement were analyzed.…”

Section: Introductionmentioning

confidence: 99%

“…Also the problems of stability and behaviour under thermo-mechanical and mechanical stresses, (see e.g. Benall and Bigoni, [11]; Candija and Brnic, [13]; Epstein and Maugin, [15]; Lehmann, [19]; Marakin and Sokolova, [21]; Simo and Miehe, [32]; Srinivasa, [25]) were analyzed. The majority of the papers describing large deformations in thermo-elastoplasticity use the method of inner parameters in the frame of thermodynamics of non-reversible processes.…”

Section: Introductionmentioning

confidence: 99%

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On the Uniqueness Conditions and Bifurcation Criteria in Coupled Thermo-Elasto-Plasticity

Śloderbach¹

2017

International Journal of Applied Mechanics and Engineering

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The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermo-elastoplasticity. This paper is a continuation of some previous works by the author, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermal elastoplastic coupling effects, nonassociated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. The paper contains four Appendices A, B, C and D where the local necessery and sufficient conditions of uniqueness have been derived.Key words: bifurcation of the equilibrium state, conditions and criteria of uniqueness, boundary-value problem, generalized coupled thermo-elasto-plasticity, comparison bodies, family of local conditions of uniqueness, parameter of the optimization.

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On the simulation of plastic forming under consideration of thermal effects

Shutov¹,

Ihlemann

2011

Materialwissenschaft Werkst

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A new model of finite strain thermo-viscoplasticity is constructed. The model takes a combined nonlinear isotropic-kinematic hardening into account in a thermodynamically consistent manner. The yield stress and some of the hardening parameters are temperature dependent. The equation of the heat conduction is obtained directly using the energy balance. In particular, the thermoelastic effect and the mechanical dissipation are obtained in a natural way. Unlike the classical Taylor-Quinney rule, which yields in the case of a strong kinematic hardening inconsistent simulation results, the developed model enables physically reasonable computations. In order to capture the energy storage associated with the inelastic deformation more precisely, an additional component of the free energy -the so-called detached free energy -is introduced. Using this constitutive assumption, a better fitting of the model prediction concerning the real temperature evolution can be achieved.Keywords: thermo-plasticity / viscoplasticity / large strains / kinematic hardening / detached free energy / Ein neues Modell der Thermoviskoplastizität bei finiten Deformationen wurde konstruiert. Mit dem Modell wird eine kombinierte nichtlineare isotrop-kinematische Verfestigung auf eine thermodynamisch konsistente Weise berücksichtigt. Die Fließspannung und einige der Verfestigungsparameter sind temperaturabhängig. Die Wärmeleitungsgleichung wurde direkt aus der Energiebilanz abgeleitet. Dabei wurden der thermoelastische Effekt und die mechanische Dissipation auf einem natürlichen Wege erhalten. Im Gegensatz zum klassischen Taylor-Quinney-Ansatz, der bei großer kinematischer Verfestigung auf inkonsistente Simulationsergebnisse führt, werden mit dem entwickelten Materialmodell physikalisch sinnvolle Berechnungen ermöglicht. Mit dem Ziel, die Energiespeicherung infolge inelastischer Vorgänge noch genauer zu erfassen, wurde eine zusätzliche Komponente der freien Energie eingeführt -die sogenannte abgetrennte freie Energie. Mit dieser konstitutiven Annahme kann eine bessere Anpassung der Modellvorhersage bezüglich der tatsächlichen Temperaturentwicklung erreicht werden.

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Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters

Cited by 50 publications

References 33 publications

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

On the Uniqueness Conditions and Bifurcation Criteria in Coupled Thermo-Elasto-Plasticity

On the simulation of plastic forming under consideration of thermal effects

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