Meshfree simulation of metal cutting: an updated Lagrangian approach with dynamic refinement

An incremental constitutive relation of friction contact is presented for large deformation analysis. After a brief review of published explanations of friction, a model is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and nonlocal effects are discussed. Formulations of a quasistatic boundary value problem based on the updated Lagrangian approach are summarized. The elastoplastic material is assumed to behave according to the generalized Prandtl-Reuss constitutive equation. Finite element methods are employed to solve the problem. Two examples are selected to demonstrate the capability and adequacy of the proposed model.

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A Comparison of EFGM and FEM for Nonlinear Solid Mechanics Problems

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.535-536.434 ◽

2013 ◽

Vol 535-536 ◽

pp. 434-437

Author(s):

Rajesh Kumar ◽

Indra Vir Singh ◽

B.K. Mishra ◽

R. Cardoso ◽

J.W. Yoon

Keyword(s):

Solid Mechanics ◽

Plastic Material ◽

Isotropic Hardening ◽

Test Problems ◽

Flow Rule ◽

Stress Strain Relation ◽

Nonlinear Solid Mechanics ◽

Updated Lagrangian Approach ◽

Updated Lagrangian ◽

Element Free

In this paper, element free Galerkin method (EFGM) has been applied to solve nonlinear solid mechanics problems using updated Lagrangian approach. The nonlinear equations have been solved using Newton Raphson method. An associative J2 flow rule and isotropic hardening has been used for the modelling of elasto-plastic material behaviour. Elastic predictor and plastic corrector algorithm has been used for the integration of incremental stress-strain relation. Few test problems involving large deformations have been simulated and the results obtained by EFGM have been compared with those obtained by FEM.

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A natural element updated Lagrangian approach for modelling fluid structure interactions

European Journal of Computational Mechanics ◽

10.13052/remn.16.323-336 ◽

2007 ◽

pp. 323-336

Author(s):

Andrés Galavís ◽

David González ◽

Elias Cueto ◽

Francisco Chinesta ◽

Manuel Doblaré

Keyword(s):

Stokes Equations ◽

Theoretical Description ◽

Navier Stokes ◽

Fluid Structure Interactions ◽

Navier Stokes Equations ◽

Fluid Structure ◽

Lagrangian Framework ◽

Natural Element ◽

Updated Lagrangian Approach ◽

Updated Lagrangian

In this paper we present a novel methodology for the numerical simulation of fluid structure interactions in the presence of free surfaces. It is based on the use of the Natural Element Method (NEM) in an updated Lagrangian framework, together with the integration of the Navier-Stokes equations by employing a Galerkin-characteristics formulation. Tracking of the free-surface is made by employing shape constructors, in particular α- shapes. A theoretical description of the method is made and also some examples of the performance of the technique are included.

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An Adaptive Local Meshfree Updated Lagrangian Approach for Large Deformation Analysis of Metal Forming

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.97-101.2664 ◽

2010 ◽

Vol 97-101 ◽

pp. 2664-2667 ◽

Cited By ~ 1

Author(s):

Yuan Tong Gu

Keyword(s):

Large Deformation ◽

Metal Forming ◽

Meshfree Methods ◽

Superior Performance ◽

Deformation Analysis ◽

Large Deformation Analysis ◽

Good Potential ◽

Updated Lagrangian Approach ◽

Updated Lagrangian ◽

Large Deformation Problems

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

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