3D Adaptive Remeshing Procedure and its Application to Large Deformation Problems

Metal orthogonal cutting and blanking are two important forming processes which include material removing. During finite element analyzing, the nonlinear problems of boundary, material and geometry must be considered to obtain the accurate calculating results. In this paper, we present an advanced adaptive remeshing procedure which has the capacities to simulate material removing processes in three dimensions. The sizes of finite elements are well adapted to local conditions which have the high distributions of physical fields using priori and posteriori error estimates. Based on constraint Delaunay Kernel, the unit mesh strategy is proposed to improve the mesh quality. By optimizing of both mesh edges and mesh elements, the mesh shape qualities are strictly controlled as the regular tetrahedrons. In this paper, Johnson-cook model is considered to simulate the elastic-visco-plastical material behaviors. The damage initiation is also judged by Johnson-cook criterion. The finite elements which reach the criterion will be killed and the material removing processes finished step by step. The proposed adaptive remeshing scheme is well present using the simulation of metal orthogonal cutting, milling and blanking processes.

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Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.865.325 ◽

2017 ◽

Vol 865 ◽

pp. 325-330 ◽

Cited By ~ 1

Author(s):

Vladimir I. Andreev ◽

Lyudmila S. Polyakova

Keyword(s):

Numerical Method ◽

Nonlinear Problems ◽

Successive Approximations ◽

Method Of Successive Approximations ◽

Deformation Diagram ◽

Method Of Solution ◽

Properties Of Materials ◽

Physical Fields ◽

Cylinders And Spheres ◽

Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

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Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2010.03.024 ◽

2011 ◽

Vol 200 (37-40) ◽

pp. 2782-2795 ◽

Cited By ~ 42

Author(s):

Linda El Alaoui ◽

Alexandre Ern ◽

Martin Vohralík

Keyword(s):

Error Estimates ◽

A Posteriori Error Estimates ◽

Nonlinear Problems ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

Linearization Errors

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MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513500486 ◽

2013 ◽

Vol 24 (01) ◽

pp. 113-144 ◽

Cited By ~ 1

Author(s):

MARKUS AURADA ◽

JENS M. MELENK ◽

DIRK PRAETORIUS

Keyword(s):

Mixed Finite Element ◽

Large Body ◽

Mixed Finite Element Method ◽

Adaptive Strategy ◽

Posteriori Error ◽

Higher Order ◽

Three Dimensions ◽

Macroscopic Model ◽

Error Estimator ◽

Discrete Problem

We introduce a stabilized conforming mixed finite element method for a macroscopic model in micromagnetics. We show well-posedness of the discrete problem for higher order elements in two and three dimensions, develop a full a priori analysis for lowest order elements, and discuss the extension of the method to higher order elements. We introduce a residual-based a posteriori error estimator and present an adaptive strategy. Numerical examples illustrate the performance of the method.

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Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

Acta Mechanica ◽

10.1007/s00707-020-02857-7 ◽

2020 ◽

Author(s):

E. Carrera ◽

◽

A. Pagani ◽

R. Augello

Keyword(s):

Finite Elements ◽

Large Deflection ◽

Nonlinear Problems ◽

Structural Domain ◽

Fe Model ◽

Efficient Manner ◽

Cross Sectional ◽

Thin Walled Structures ◽

Post Buckling ◽

Thin Walled

AbstractIn the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

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Simulation of Sheet Metal Forming Processes Using a Fully Rheological-Damage Constitutive Model Coupling and a Specific 3D Remeshing Method

Metals ◽

10.3390/met8120991 ◽

2018 ◽

Vol 8 (12) ◽

pp. 991 ◽

Cited By ~ 2

Author(s):

Abel Cherouat ◽

Houman Borouchaki ◽

Zhang Jie

Keyword(s):

Finite Element ◽

Sheet Metal ◽

Sheet Metal Forming ◽

Constitutive Equations ◽

Metal Forming ◽

Damage Mechanics ◽

Three Dimensions ◽

Automatic Process ◽

Adaptive Remeshing ◽

Fully Coupled

Automatic process modeling has become an effective tool in reducing the lead-time and the cost for designing forming processes. The numerical modeling process is performed on a fully coupled damage constitutive equations and the advanced 3D adaptive remeshing procedure. Based on continuum damage mechanics, an isotropic damage model coupled with the Johnson–Cook flow law is proposed to satisfy the thermodynamic and damage requirements in metals. The Lemaitre damage potential was chosen to control the damage evolution process and the effective configuration. These fully coupled constitutive equations have been implemented into a Dynamic Explicit finite element code Abaqus using user subroutine. On the other hand, an adaptive remeshing scheme in three dimensions is established to constantly update the deformed mesh to enable tracking of the large plastic deformations. The quantitative effects of coupled ductile damage and adaptive remeshing on the sheet metal forming are studied, and qualitative comparison with some available experimental data are given. As illustrated in the presented examples this overall strategy ensures a robust and efficient remeshing scheme for finite element simulation of sheet metal‐forming processes.

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Rigorous and effective a-posteriori error bounds for nonlinear problems—application to RB methods

Advances in Computational Mathematics ◽

10.1007/s10444-020-09741-x ◽

2020 ◽

Vol 46 (2) ◽

Author(s):

Andreas Schmidt ◽

Dominik Wittwar ◽

Bernard Haasdonk

Keyword(s):

Error Bounds ◽

Nonlinear Problems ◽

Posteriori Error ◽

A Posteriori ◽

A Posteriori Error ◽

A Posteriori Error Bounds

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Solution of the Inverse Elastography Problem in Three Dimensions for a Parametric Class with A Posteriori Error Estimation

Moscow University Physics Bulletin ◽

10.3103/s0027134919050096 ◽

2019 ◽

Vol 74 (5) ◽

pp. 488-493

Author(s):

A. S. Leonov ◽

A. N. Sharov ◽

A. G. Yagola

Keyword(s):

Error Estimation ◽

Posteriori Error ◽

A Posteriori Error Estimation ◽

Three Dimensions ◽

A Posteriori ◽

Posteriori Error Estimation ◽

A Posteriori Error ◽

Parametric Class

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Analysis of Dynamic Response for Piezoelectric Vibration Converter by Finite Element Simulation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.336-338.335 ◽

2007 ◽

Vol 336-338 ◽

pp. 335-337

Author(s):

Xiang Cheng Chu ◽

Ren Bo Yan ◽

Wen Gong ◽

Long Tu Li

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Finite Elements ◽

Dynamic Response ◽

Finite Element Modeling ◽

Three Dimensions ◽

Dynamic Motion ◽

Element Simulation ◽

Piezoelectric Coupling ◽

Piezoelectric Vibration

The dynamic behavior of a vibration converter of an ultrasonic motor is described using finite element method. Tetrahedral finite elements with three dimensions are formulated with the effects of piezoelectric coupling. And the solution of the coupled electroelastic equations of dynamic motion is presented. The simulated response of the vibration converter is calculated, and shows excellent consistency with experimental results, which proved that finite element modeling is a good approach to optimize piezoelectric apparatus design. A gradual optimized method is employed to ascertain the most compatible structure.

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