An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory

Khoei, A.R.; Karimi, Kaivan

doi:10.1016/j.commatsci.2008.05.019

Cited by 49 publications

(17 citation statements)

References 44 publications

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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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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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“…Khoei and Karimi [4] proposed the combined Cosserat/XFEM model to simulate the strain localization in elasto-plastic solids. They enriched normal to the discontinuity displacement and assumed the tangential displacement and micro-rotations to be continuous.…”

Section: Cosserat Models Coupled With the Extended Finite Element Methodsmentioning

confidence: 99%

“…In his works, he classified human and bovine bones as a Cosserat material, conducted experimental research on the Cosserat elastic parameters, and proved the advantages of the Cosserat theory over the classical theory for describing the materials with a complex microstructure. Later, the invention of such powerful technique as the Finite Element Method (FEM) made it possible to conduct the numerical modelling of Cosserat materials behaviour, although mostly in the geomechanical area [3,4,5,6]. …”

Section: Introductionmentioning

confidence: 99%

Simulation of cracks in a Cosserat medium using the extended finite element method

Kapiturova

Gracie

Potapenko

2014

Mathematics and Mechanics of Solids

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This research investigates fracture behaviour in the Cosserat materials. The Cosserat elasticity description of the materials incorporates a characteristic length scale (e.g. grains, particles, fibres, etc.) into the model. The characteristic length scale in such materials is known to significantly influence the macroscopic behaviour of the whole body. Simulation of the fracture processes, such as crack opening and propagation, in Cosserat materials still remains a challenge for the scientific community. The goal of this thesis is to propose and validate a two dimensional extended finite element method model of edge cracks within the Cosserat elasticity theory framework.The crack modelling was conducted using the Finite Element Method (FEM) and eXtended Finite Element Method (XFEM) implemented in the Matlab code. The strong and weak formulations of the problem and the discrete XFEM equations are presented in the thesis. Mode I and II edge crack models in a Cosserat medium are discussed and verified through a series of patch and convergence tests. In addition, the numerical evaluation of the J-integral for the Cosserat medium is presented, and the J-integral for the Cosserat medium is compared to the J-integral for the classical elasticity.The XFEM/Cosserat method is shown to be robust and able to effectively model the edge crack problems in a Cosserat medium. Moreover, the elastic parameter α is found to be a powerful coupling tool between the microrotations and the translations. The Cosserat J-integral differs from the classical J-integral by 2% to 40%, for a given crack depending on the micropolar elastic coupling constant α.iii Acknowledgements I would like to thank my supervisors, Dr. Robert Gracie and Dr. Stanislav Potapenko, for their guidance and support during my study at the University of Waterloo.

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“…An overview of the technique was addressed by Bordas et al [36] in the framework of an object-oriented-enriched finite element programming. The X-FEM was employed in elasto-plasticity problems, including: the crack propagation in plastic fracture mechanics [37,38], the plasticity of frictional contact on arbitrary interfaces [39,40], the large X-FEM deformation [41,42], the ALE-XFEM model for large plastic deformation [43,44], the localization phenomenon in higher-order Cosserat theory [45].…”

Section: Introductionmentioning

confidence: 99%

Extended finite element modeling of deformable porous media with arbitrary interfaces

Khoei

Haghighat

2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, an enriched finite element method is presented for numerical simulation of saturated porous media. The arbitrary discontinuities, such as material interfaces, are encountered via the extended finite element method (X-FEM) by enhancing the standard FEM displacements. The X-FEM technique is applied to the governing equations of porous media for the spatial discretization, followed by a generalized Newmark scheme used for the time domain discretization. In X-FEM, the material interfaces are represented independently of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, several numerical examples are analyzed, including the dynamic analysis of the failure of lower San Fernando dam, to demonstrate the efficiency of the X-FEM technique in saturated porous soils.

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An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory

Cited by 49 publications

References 44 publications

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

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

Simulation of cracks in a Cosserat medium using the extended finite element method

Extended finite element modeling of deformable porous media with arbitrary interfaces

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