Extended finite element method in plasticity forming of powder compaction with contact friction

Khoei, A.R.; Shamloo, Amir; Azami, A.R.

doi:10.1016/j.ijsolstr.2005.11.008

Cited by 59 publications

(32 citation statements)

References 54 publications

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“…In the global approach, the slip degree of freedom is interpolated through the introduction of additional global degrees of freedom to existing nodes surrounding the crack. The latter class of methods are often called the extended FE methods [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. A third class of approach, based on non-linear contact mechanics, applies to the case where the crack geometry is known a priori so that the element sides can be aligned to the crack [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

A contact algorithm for frictional crack propagation with the extended finite element method

Liu¹,

Borja²

2008

Numerical Meth Engineering

154

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SUMMARYWe present an incremental quasi-static contact algorithm for path-dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from nonlinear contact mechanics and embedded within a localized element by penalty method. Newton-Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called 'LATIN' for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution.

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Section: Introductionmentioning

confidence: 99%

A contact algorithm for frictional crack propagation with the extended finite element method

Liu¹,

Borja²

2008

Numerical Meth Engineering

154

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“…They noted the superior rates of convergence for the penalty method compared to the LATIN method. The approach has been extended to problems with bulk plasticity (Khoei et al, 2006;Liu and Borja, 2009) and large sliding contact (Khoei and Mousavi, 2010;Liu and Borja, 2010a). It should be noted that these approaches still represent a regularization of a discrete formulation that is unstable, and involve a free penalty parameter.…”

Section: Introductionmentioning

confidence: 99%

An efficient finite element method for embedded interface problems

Dolbow

Harari

2008

Numerical Meth Engineering

218

223

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We focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interafces.We begin by examining embedded Dirichlet problems -a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers, and stabilized methods, based on Nitsche's approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche's approach. We address the incompatibility of Nitsche's method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumping procedure.We revisit Nitsche's method and inspect the effect of this modified variational iv form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz. stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear, frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche's method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the proposed choice of weighting and stabilization parameters, Nitsche's method achieves the right balance between accurate constraint enforcement and flux recovery -a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.v To Amma (mom) and Nannagaru (dad), vi

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“…However, less X-FEM modeling has been reported in elastoplasticity. Maximum implementation of X-FEM in plasticity problems are found in the following: plasticity forming of powder compaction [65], plasticity of frictional contact on arbitrary interfaces [66,67], large X-FEM deformation [68,69], ALE-X-FEM model for large plastic deformation [29,70], localization phenomenon in higher order Cosserat theory [71], crack propagation in plastic fracture mechanics [72,73], and elastoplastic fatigue crack growth [74].…”

Section: Enriched Ale Finite Element Methodsmentioning

confidence: 99%

Modeling of Powder Forming Processes; Application of a Three‐Invariant Cap Plasticity and an Enriched Arbitrary Lagrangian–Eulerian FE Method

Khoei

2010

Advanced Computational Materials Modeling

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Powder metallurgy is a highly developed method of manufacturing reliable ferrous and nonferrous parts. The powder metallurgy process is cost-effective, because it minimizes machining, produces good surface finish, and maintains close dimensional tolerances. The method is a material-processing technique utilized to achieve a coherent near-to-net shape industrial component. The often extremely high tolerance requirements of the parts and the cost for hard machining of a sintered component are a challenge for die pressing. One of the main difficulties that exists in the compaction-forming process of powders includes a nonhomogeneous density distribution, which has wide ranging effects on the final performance of the compacted part. The variation of density results in cracks and also in localized deformation in the compact, producing regions of high density surrounded by lower density material, leading to compact failure. The lack of homogeneity is primarily caused by friction, due to interparticle movement, as well as relative slip between powder particles and the die wall. The die geometry and the sequence of movement result in a lack of homogeneity of density distribution in a compact. Thus, the success of compaction forming depends on the ability of the process in imparting a uniform density distribution in the engineered part. In order to perform such analysis, the complex mechanisms of compaction process must be drawn into a mathematical formulation with the knowledge of material behavior.A number of constitutive models have been developed for the compaction of powders over the last three decades, including micromechanical models [1-3], flow formulations [4], and solid mechanics models [5][6][7][8][9][10][11]. The porous material model, generally known as a modified von Mises criterion [12], has been used for the simulation of powder-forming processes. This model includes the influence of the hydrostatic stress component, and satisfies the symmetry and convexity conditions required for the development of a plasticity theory. The yielding of porous materials is more complicated than that of fully dense materials, because the onset of yielding is influenced not only by the deviatoric stress components

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Extended finite element method in plasticity forming of powder compaction with contact friction

Cited by 59 publications

References 54 publications

A contact algorithm for frictional crack propagation with the extended finite element method

A contact algorithm for frictional crack propagation with the extended finite element method

An efficient finite element method for embedded interface problems

Modeling of Powder Forming Processes; Application of a Three‐Invariant Cap Plasticity and an Enriched Arbitrary Lagrangian–Eulerian FE Method

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