Thermal Effects in Plasticity. Part II: Uniqueness and Applications

Raniecki, B.; Sawczuk, A.

doi:10.1002/zamm.19750550703

Cited by 12 publications

(21 citation statements)

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“…2. There are papers concerning problems of solution of uniqueness and bifurcation of equilibrium states (see Raniecki and Mróz,[4], [5]; Raniecki, [6], [33]; Raniecki and Sawczuk, [36]; Raniecki and Bruhns, [34]; Śloderbach, [1], [3]). In this paper, however, a new global and local criterion was formulated for the derived comparison body dependent on statically permissible velocity fields of stress.…”

Section: Discussionmentioning

confidence: 99%

“…The inequalities (2.5) and (2.6) are a generalization of the uniqueness conditions derived by Mróz and Raniecki [4], [5], Raniecki, [6], Raniecki and Sawczuk, [35], [36]. This generalization consists in the non-associated laws of plastic flow being taken into account as well as the influence of plastic deformations on the thermoelastic properties of the body.…”

Section: Uniqueness Solution Of Incremental Problems For Homogenous Pmentioning

confidence: 90%

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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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Section: Discussionmentioning

confidence: 99%

Section: Uniqueness Solution Of Incremental Problems For Homogenous Pmentioning

confidence: 90%

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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“…Satisfying the set of field and constitutive equations of (cf. [1,3,4,7,15,21,47 It is easy to see that if a solution of the problems (a 1 ) and (a 2 ) is to be unique, it is necessary that the following respective conditions known from the isothermal theory of plasticity should be satisfied [1,3,4,7,13,14,16,47] h > 0 and h + g p : MF σ > 0, (2.37)whereh is the isothermal strain-hardening function obtained in [1,2,7],∂σ , b is the function describing evolution of internal parametersK [1,2,46,47]. For the problems (a 1 ) and (a 2 ), conditions (2.37) are also sufficient.…”

mentioning

confidence: 99%

“…The necessary uniqueness conditions for the problems (b 1 ) and ( b 2 ) have the following forms [1,3,7,16,47]:…”

mentioning

confidence: 99%

“…[1,3,4,6,7,16,21,47] when all the elastic-plastic coupling effects being rejected (γ 9 =γ 9 = γ 10 =γ 10 = γ 11 =γ 11 = γ 12 =γ 12 = 0). By analysing the cyclic isothermal process in the space of stresses, authors of works [1,3,6,7,16,21,47] have appointed on base of account that for the majority of materials (in particular for metallic materials) m σ is in general positiveThe inequalities (2.39) and (2.40) are a generalization of the uniqueness conditions appropriately derived by Mróz, Raniecki and Sawczuk, see [4,6,7,16] for the case of associated flow laws and without a elasticplastic coupling effects. This generalization consists in the non-associated laws of plastic flow being taken into account as well as the influence of plastic deformations on the thermoelastic properties of the body.…”

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confidence: 99%

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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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Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

Semnani

White

Borja

2016

Num Anal Meth Geomechanics

125

105

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SUMMARYGeomaterials such as soils and rocks are inherently anisotropic and sensitive to temperature changes caused by various internal and external processes. They are also susceptible to strain localization in the form of shear bands when subjected to critical loads. We present a thermoplastic framework for modeling coupled thermomechanical response and for predicting the inception of a shear band in a transversely isotropic material using the general framework of critical state plasticity and the specific framework of an anisotropic modified Cam-Clay model. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Subsequently, stresspoint simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermomechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation.

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Thermal Effects in Plasticity. Part II: Uniqueness and Applications

Cited by 12 publications

References 11 publications

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

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

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

Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity

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