2D Meshless Solution of Elastoplastic with Damage Problem

2012 ◽  
Vol 504-506 ◽  
pp. 413-418 ◽  
Author(s):  
Zohra Sendi ◽  
Carl Labergère ◽  
Khemais Saanouni ◽  
Hedi Belhadj Salah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computing Time ◽  
Least Square ◽  
Ductile Damage ◽  
Isotropic Hardening ◽  
The Finite Element Method ◽  
Time Step ◽  
Moving Least Square ◽  
Element Method

The Finite Element Method (FEM) is today the most widely used in numerical simulation of forming processes, due essentially to the continuous improvement of the FEM over the years and the simplicity of its implementation. However, this method has some limitations such as the distortion of elements under large inelastic deformation and the influence of the mesh on the results in several applications. The simulation of metal forming process with large plastic strain is a classical example where the successive remeshing is often the proposed solution in this case. But the remeshing raises the problems of precision and computing time. In this context and in order to avoid the remeshing process, a Meshless method is experimented in the solving of an elastoplastic problem coupled to the isotropic ductile damage. An Element Free Galerkin (EFG) method based on Moving Least Square (MLS) concept is considered in this proposal. A two-dimensional Mechanical problem was studied and solved by a Dynamic-Explicit resolution scheme where the material behaviour is based on an isotropic hardening fully coupled to ductile damage model. In a first step a parametric study is conducted in order to find the most influent parameters on the accuracy of the results. The effect of the number of nodes, of support nodes, of quadrature points, the effect of the time-step and the support domain size are analysed and optimal values are found. In a second step, the meshless results are compared with those of the finite element method and some concluding remarks relative to the accuracy and the computing time are given.

scholarly journals Identification of elastic-plastic behavior in AHSS using the isotropic hardening model by the finite element method and EBSD

2019 ◽  
Vol 6 (5) ◽  
pp. 649-658
Author(s):  
Érika Aparecida da Silva ◽  
Marcelo dos Santos Pereira ◽  
Jean Pierre Faye ◽  
Rosinei Batista Ribeiro ◽  
Nilo Antonio de Sousa Sampaio ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isotropic Hardening ◽  
Plastic Behavior ◽  
The Finite Element Method ◽  
Hardening Model ◽  
Elastic Plastic ◽  
Element Method

scholarly journals Determining the stress concentration change with time in a viscoelastic orthotropic solid

2020 ◽  
pp. 28-34
Author(s):  
M.F. Selivanov ◽  
◽  
Y.R. Kulbachnyy ◽  
D.R. Onishchenko ◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Stiffness Matrix ◽  
Orthotropic Material ◽  
Orthotropic Plate ◽  
Round Hole ◽  
The Finite Element Method ◽  
Time Step ◽  
Element Method

The procedure for solving the plane problem of the linear theory of viscoelasticity by the finite element method is described. Based on the virtual work principle and the assumption of the constancy of the strain rate at small intervals of time, the matrix form of the equilibrium equations of the finite-element approximation of a body is written. The solution procedure is described for the constitutive relations in the Boltzmann—Volterra integral form. This integral is transformed into an incremental form on a time mesh, at each interval of which the problem is solved by the finite element method with unknown increments of displacements. The numerical procedure is constructed by ununiformly dividing the time interval, at which the study is conducted. In this case, the stiffness matrix requires recalculation at each time step. The relaxation functions of the moduli of a viscoelastic orthotropic material are described in the form of the Proni—Dirichlet series. The solution to the problem of determining the change over time of the stress concentration in a body with a round hole in a viscoelastic orthotropic plate is presented. To construct a numerical solution, the three moduli of orthotropic material were written using one exponent with the same relaxation time. For these initial data, an analytic expression for the viscoelastic components of the stiffness matrix of an orthotropic plate under plain stress conditions is constructed. Numerical examples are presented for several ratios of the hole radius to the size of the plate. These results are compared with the solution obtained for an infinite plate by inverse transformation by a numerical method of the well-known analytic elastic solution.

A Finite Element Solution of the Unidimensional Shallow-Water Equation

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Ali Triki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Shallow Water ◽  
Rectangular Channel ◽  
Shallow Water Equation ◽  
The Finite Element Method ◽  
Time Step ◽  
Text Book ◽  
Element Method

Based on the finite element method, the numerical solution of the shallow-water equation for one-dimensional (1D) unsteady flows was established. To respect the stability criteria, the time step of the method was dependent on the space step and flow velocity. This method was used to avoid the restriction due to the wave celerity variation in the computational analysis when using the method of characteristics. Furthermore, boundary conditions are deduced directly from the scheme without using characteristics equations. For the numerical solution, a general-purpose computer program, based on the finite element method (FEM), is coded in fortran to analyze the dynamic response of the open channel flow. This program is able to handle rectangular, triangular, or trapezoidal sections. Some examples solved with the finite element method are reported herein. The first involves routing a discharge hydrograph down a rectangular channel. The second example consists of routing a sudden shutoff of all flow at the downstream end of a rectangular channel. The third one deals with routing a discharge hydrograph down a trapezoidal channel. These examples are taken from the quoted literature text book. Numerical results agree well with those obtained by these authors and show that the proposed method is consistent, accurate, and highly stable in capturing discontinuities propagation in free surface flows.

scholarly journals Energy Resolved Neutron Imaging for Strain Reconstruction Using the Finite Element Method

2020 ◽  
Vol 6 (3) ◽  
pp. 13
Author(s):  
Riya Aggarwal ◽  
Michael H. Meylan ◽  
Bishnu P. Lamichhane ◽  
Chris M. Wensrich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Square Method ◽  
Neutron Imaging ◽  
Least Square ◽  
The Finite Element Method ◽  
Cantilevered Beam ◽  
Element Approach ◽  
Tikhonov Regularisation ◽  
Element Method

A novel pulsed neutron imaging technique based on the finite element method is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. The finite element approach used to reconstruct the strain uses the least square method constrained by the conditions of equilibrium. This inclusion of equilibrium makes the problem well-posed. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug sample, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a Tikhonov regularisation scheme further improves the reconstruction.

scholarly journals Propagation of a Crack in a Composite Plate

2018 ◽  
Vol 55 (2) ◽  
pp. 179-183
Author(s):  
Ionel Iacob ◽  
Ionel Chirica ◽  
Elena Felicia Beznea
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Composite Plate ◽  
Extended Finite Element Method ◽  
Fem Analysis ◽  
The Finite Element Method ◽  
Extended Finite Element ◽  
Time Step ◽  
Element Method

In this paper, a model of a composite plate with a central elliptical cut-out and with an initial fissure was subjected to a tension load in the finite element method (FEM) software Abaqus to observe the propagation of that crack during a certain amount of time that elapsed in the FEM analysis. Due to symmetry, only half of the plate was modeled, as a shell, and the extended finite element method (XFEM) was used for the crack. The material properties that were assigned to the plate were taken from the database of the Ansys Mechanical software. In the vicinity of the crack a finer mesh was applied to be able to better observe the evolution of the fissure and the changes of the Von Misses stress graphs for each time step of the analysis.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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