Geometrical material structure of elastoplasticity

Maugin, Gérard A.; Epstein, Marcelo

doi:10.1016/s0749-6419(97)00043-0

Cited by 50 publications

(40 citation statements)

References 16 publications

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“…We see now thatḊ = DL D and therefore we get the relation between the material strain rate tensor and the material velocity L D used in [1,25,29] and other papers.…”

Section: This Velocity Is Related To the Velocity Lmentioning

confidence: 84%

“…Such a relation was first studied in [29]. In particular, the relation between the inhomogeneity velocity gradient L P (see below) and the plastic distortion ratė L =Ḟ p · (F p ) −1 was introduced.…”

Section: Ciancio M Dolfin M Francaviglia and S Prestonmentioning

confidence: 99%

“…For convenience we identify the "archetype" space V (see [12,29]) with the tangent space at the origin O of the physical space: V = T O (R 3 ) and its metric with the metric h at the origin.…”

Section: Materials and Physical Spacesmentioning

confidence: 99%

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Uniform Materials and the Multiplicative Decomposition of the Deformation Gradient in Finite Elasto-Plasticity

Ciancio

Dolfin

Francaviglia

et al. 2008

Journal of Non-Equilibrium Thermodynamics

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Abstract.In this work we analyze the relation between the multiplicative decomposition F = F e F p of the deformation gradient as a product of the elastic and plastic factors ([12, 17, 18, 26]) and the theory of uniform materials ([33, 40, 41]). We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations -total φ and the inelastic φ 1 .We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations (φ, φ 1 ) and the material metric g.Finally the dissipative inequality for the materials of this type is presented. It is shown that the conditions of positivity of the internal dissipation terms related to the processes of plastic and metric evolution provide the anisotropic yield criteria.

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“…We see now thatḊ = DL D and therefore we get the relation between the material strain rate tensor and the material velocity L D used in [1,25,29] and other papers.…”

Section: This Velocity Is Related To the Velocity Lmentioning

confidence: 84%

Section: Ciancio M Dolfin M Francaviglia and S Prestonmentioning

confidence: 99%

See 1 more Smart Citation

Uniform Materials and the Multiplicative Decomposition of the Deformation Gradient in Finite Elasto-Plasticity

Ciancio

Dolfin

Francaviglia

et al. 2008

Journal of Non-Equilibrium Thermodynamics

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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%

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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“…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].…”

mentioning

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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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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Geometrical material structure of elastoplasticity

Cited by 50 publications

References 16 publications

Uniform Materials and the Multiplicative Decomposition of the Deformation Gradient in Finite Elasto-Plasticity

Uniform Materials and the Multiplicative Decomposition of the Deformation Gradient in Finite 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

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