A nonlinear numerical analysis for metal-forming process using the rigid-(visco)plastic element-free Galerkin method

Yanjin, Guan; Wu, Xiaohu; Zhao, Guoqun; Lü, Peng

doi:10.1007/s00170-008-1585-3

Cited by 17 publications

(4 citation statements)

References 27 publications

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“…A large number of techniques have been proposed from time to impose the boundary conditions such as Lagrange multiplier method [16], modified variational principle [17], and coupling of FE-EFG [18]. EFGM has found application mainly in the areas of fracture mechanics [19,20], metal forming [21], vibration analysis [22], heat transfer [23], contact analysis [24] and extrusion processes [25]. EFGM has also been successfully used to analyse three-dimensional fracture mechanics problems [26,27] and bi-material interface cracks [28].…”

Section: Introductionmentioning

confidence: 99%

Fatigue crack growth in presence of material discontinuities by EFGM

Jameel

Harmain

2015

International Journal of Fatigue

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Section: Introductionmentioning

confidence: 99%

Fatigue crack growth in presence of material discontinuities by EFGM

Jameel

Harmain

2015

International Journal of Fatigue

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“…As shown in the table.2, the size of the ball after two methods of numerical simulation is smaller than the experimental data. The reason may be that the friction between the billet and the mold in the experiment condition is more complicated [4] .…”

Section: The Experimental Data and Simulation Data Contrast The Techn...mentioning

confidence: 99%

Element-Free Galerkin Method of Cold Forging Steel Ball

Yuan

Liu

2014

AMR

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The fundamental principle of three dimensional Element-free Galerkin has been briefly investigated in this paper, and built forming mode of steel ball cold forging, Element-free Galerkin method successfully applied to the simulation analysis of steel ball cold forging forming process in the LS-DYNA simulation software. In comparison to Finite Element Method and experiment data, Proved Element-free Galerkin method was feasible in metal plastic forming process, and in the large deformation simulation was more accurate than the finite element method, Element-free Galerkin method has more obvious advantages after altering the impact factors.

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“…These shape functions do not satisfy the Kronecker delta property; hence, the boundary conditions are applied by the techniques such as Lagrange multiplier approach, modified variational principle approach, coupling FE shape functions with MLS approximations . Till date, the EFG method has been widely used to model the various problems in different areas such as linear elasticity, static and dynamic fracture, metal forming, vibration, heat transfer, plate and shell analysis, 3D fracture . In mesh‐free methods such as EFG, the approximation is performed using a set of scattered nodal points in the domain of interest; hence, it does not require a structured mesh.…”

Section: Introductionmentioning

confidence: 99%

A coupled FE–EFG approach for modelling crack growth in ductile materials

Shedbale

Singh

Mishra

2016

Fatigue Fract Eng Mat Struct

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A B S T R A C T In this work, a coupled finite element-element free Galerkin approach has been used to model crack growth in ductile materials under monotonic and cyclic loads. In this approach, a small discontinuous domain near crack is modelled by EFG method, whereas the rest of the domain is modelled by FEM to exploit the advantages of both the methods. A ramp function has been used in the transition region to maintain the continuity between FE and EFG domains. Two plasticity models (GTN and von-Mises) and three hardening rules (isotropic, kinematic and mixed) have been used to model the nonlinear material behaviour. Four different problems, i.e. single edge notched tension specimen, double edge notched tension specimen, compact tension specimen and three-point bend specimen, are solved under plane strain condition using J-R curve approach. Finally, a CT specimen problem is also solved by coupled approach using three hardening rules and two plasticity models under cyclic loading.A = void nucleation parameter a = initial crack length a J = degrees of freedom associated with Heaviside function a(x) = vector of unknown coefficients b = body force vector per unit volume b α K = degrees of freedom associated with asymptotic functions B = matrix of shape functions gradients D el = elastic constitutive matrix D ep = elasto-plastic constitutive matrix E = Young's modulus E = Green-Lagrange strain tensor f = void volume fraction f * = damage parameter G = matrix of derivatives of shape functions H = hardening modulus H(x) = Heaviside function I = second order unit tensor J cr = critical J-integral K mat = material tangent stiffness matrix K geo = geometric stiffness matrix K T = total tangent stiffness matrix m = order of basis function Correspondence: I. V. Singh.

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A nonlinear numerical analysis for metal-forming process using the rigid-(visco)plastic element-free Galerkin method

Cited by 17 publications

References 27 publications

Fatigue crack growth in presence of material discontinuities by EFGM

Fatigue crack growth in presence of material discontinuities by EFGM

Element-Free Galerkin Method of Cold Forging Steel Ball

A coupled FE–EFG approach for modelling crack growth in ductile materials

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