Some computational aspects of large deformation, rate-dependent plasticity problems

Taylor, L.M.; Becker, Eric B.

doi:10.1016/0045-7825(83)90009-9

Cited by 70 publications

(23 citation statements)

References 17 publications

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“…The axisymmetric billet is a severe test problem that has been used by Taylor and Becker [68] and Simo [58]. The problem is here solved with the proposed gradient-enhanced plastic degradation model.…”

Section: Upsetting Of An Axisymmetric Billetmentioning

confidence: 99%

Strongly non‐local gradient‐enhanced finite strain elastoplasticity

Geers

Ubachs

Engelen

2003

Numerical Meth Engineering

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SUMMARYThis paper presents a gradient plasticity formulation developed in a strongly non-local format and applicable to ductile failure for ÿnite strain plasticity. The obtained formulation is an extension of a framework proposed by Simo (Computer Methods in Applied Mechanics and Engineering 1988; 66:199) into the softening and localization regime. The presented model inherits the well-established regularization properties of its strongly non-local enrichment and leads to an implicit computational scheme with a consistent tangent operator. Numerical examples are given which illustrate the strongly non-local character of the formulation, the in uence of the type of intrinsic length scale considered, as well as several topics on plastic failure initiation and evolution into the geometrically non-linear regime.

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Section: Upsetting Of An Axisymmetric Billetmentioning

confidence: 99%

Strongly non‐local gradient‐enhanced finite strain elastoplasticity

Geers

Ubachs

Engelen

2003

Numerical Meth Engineering

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“…In addition to the stress rate ( & ) Σ , we will use the Jaumann derivative of the stress tensor ( ) Σ J [14,18],…”

Section: Constitutive Relations the Stress State Is Described By Thementioning

confidence: 99%

“…(ii) methods of the second group are based on the same variational equation, but the current metric is used as a basis one [1,6,14,15,18];…”

mentioning

confidence: 99%

“…[19, 21] represent the deformation process as a sequence of equilibrium states and describe the transition from one state to another as a load increment (changed boundary conditions, domain of definition, etc.). These methods [20] can be divided [9] into three groups:(i) methods of the first group are based on the virtual-displacement principle, in which all quantities are referred to the initial undeformed state;(ii) methods of the second group are based on the same variational equation, but the current metric is used as a basis one [1,6,14,15,18];(iii) methods of the third group are based on the Lagrangian-Eulerian formulation, where the behavior of a particle (elementary volume) is described using the Lagrange method, and for the current state a plastic-flow problem is formulated according to the Euler approach [2, 3, 15-17].We will use the third approach to analyze large strains of a medium with elastic and plastic properties. In particular, we will formulate a problem of the corresponding class in the current metric for strain rates, which in combination with incremental loading and continuous geometry update will make it possible use employ the FEM.…”

mentioning

confidence: 99%

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Numerical Investigation of Large Elastoplastic Strains of Three-Dimensional Bodies

Golovanov

Sultanov

2005

Int Appl Mech

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A method of stress-strain analysis of elastoplastic bodies with large displacements, rotations, and finite strains is developed. The incremental loading technique is used within the framework of the arbitrary Lagrangian-Eulerian formulation. Constitutive equations are derived which relate the Jaumann derivative of the Cauchy-Euler stress tensor and the strain rate. The spatial discretization is based on the FEM and multilinear three-dimensional isoparametric approximation. An algorithm of stress-strain analysis of elastic, hyperelastic, and perfectly plastic bodies is given. Numerical examples demonstrate the capabilities of the method and its software implementation Keywords: three-dimensional body, large elastoplastic strains, stress-strain state, incremental loading technique, FEM Introduction. Classical Lagrangian formulations are widely used to solve nonlinear problems of solid mechanics (considering physical and geometrical nonlinearity). According to these formulations, the state of an elementary volume is described in terms of the components of the displacement vector (from the undeformed state to a deformed state) and the second Piola-Kirchhoff stress tensor, also referred to the undeformed volume. In this case, boundary-value problems can be formulated well in differential or variational form [1,4,6,8,12] and then solved using various numerical methods. However, this approach has an essential fault when strains are large. In that case, it becomes very difficult to derive constitutive relations, especially when they have differential (rate) form.Step-by-step methods (incremental loading) developed from modern numerical methods (FEM, FDM, etc.) [19, 21] represent the deformation process as a sequence of equilibrium states and describe the transition from one state to another as a load increment (changed boundary conditions, domain of definition, etc.). These methods [20] can be divided [9] into three groups:(i) methods of the first group are based on the virtual-displacement principle, in which all quantities are referred to the initial undeformed state;(ii) methods of the second group are based on the same variational equation, but the current metric is used as a basis one [1,6,14,15,18];(iii) methods of the third group are based on the Lagrangian-Eulerian formulation, where the behavior of a particle (elementary volume) is described using the Lagrange method, and for the current state a plastic-flow problem is formulated according to the Euler approach [2, 3, 15-17].We will use the third approach to analyze large strains of a medium with elastic and plastic properties. In particular, we will formulate a problem of the corresponding class in the current metric for strain rates, which in combination with incremental loading and continuous geometry update will make it possible use employ the FEM.1. Kinematics of Medium. Following the Lagrange approach, we introduce the position vector r r r x e

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“…20. The reference responses reported by Ponthot [38], Taylor and Becker [29] are considered together with the monolithic and domain decomposition tests with four and twelve decompositions, respectively. The mechanical response of the domain decomposition method does not depend of the number of decompositions and conformity of the interfaces and is in agreement with the monolithic response which, in turn, shows that the selected constitutive model matches the results provided in literature, particularly the ones by Ponthot [29].…”

Section: Coupled Thermomechanical Formulation Applied To "Bulk-forminmentioning

confidence: 99%

The domain interface method in non-conforming domain decomposition multifield problems

et al. 2016

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The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the nonconforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya-Babuška-Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.

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Some computational aspects of large deformation, rate-dependent plasticity problems

Cited by 70 publications

References 17 publications

Strongly non‐local gradient‐enhanced finite strain elastoplasticity

Strongly non‐local gradient‐enhanced finite strain elastoplasticity

Numerical Investigation of Large Elastoplastic Strains of Three-Dimensional Bodies

The domain interface method in non-conforming domain decomposition multifield problems

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