Multiscale Modeling of Large Deformation Processes in Polycrystalline Metals

2003 ◽  
Author(s):  
Antoinette Maniatty ◽  
Karel Matous ◽  
Jing Lu
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Grain Structure ◽  
Current Work ◽  
Integration Scheme ◽  
Two Dimensional ◽  
Scale Bridging ◽  
Grain Structures ◽  
Backward Euler ◽  
Bulk Response

A mesoscale model for predicting the evolution of the grain structure and the mechanical response of polycrystalline aggregates subject to large deformations, such as arise in bulk metal forming processes, is presented. The gain structures modeled are either experimentally observed or are computer generated and statistically similar to experimentally observed grain structures. In order to capture the inhomogeneous deformations and the resulting grain structure characteristics, a discretized model at the mesoscale is used. This work focuses on Al-Mg-Si alloys. Scale bridging is used to link to the macroscale. Examples involving two-dimensional grain structures and current work on three-dimensional grain structures are presented. The present work provides a framework to model the mesoscopic behavior and interactions between grains during finite strains. The mesoscale is characterized by a statistically representative voluem element (RVE), which contains the grains of a polycrystal. Experimentally observed grain structures are used both as models directly (for two-dimensional cases) and to define statistical characteristics to verify the similarity of computer generated grain structures (for three-dimensional cases). A Monte Carlo method based on the Potts model is used to define three-dimensional grain structures. In order to make the representative grain structure appropriate for scale-bridging, we design them with periodicity. A three-field, updated Lagrangian finite element formulation with a kinematic split of the deformation gradient into volume preserving and volumetric parts is used to create a stable finite element method in the context of nearly incompressible behavior. A fully implicit two-level backward Euler integration scheme is derived for integrating the constitutive equations, and consistent linearization is used in Newton’s method to solve the resulting equations. In addition, the average of the boundary conditions and bulk response must match the macroscopically measured bulk response. To illustrate and verify the proposed model, we analyze examples involving two-dimensional grain structures and compare with results from a Taylor model. Current work on three-dimensional grain structures ara also presented.

A Finite Element Procedure of a Cyclic Thermoviscoplasticity Model for Solder and Copper Interconnects

1998 ◽  
Vol 120 (1) ◽  
pp. 24-34 ◽  
Author(s):  
C. Fu ◽  
D. L. McDowell ◽  
I. C. Ume
Keyword(s):  
Finite Element ◽  
Electronic Packaging ◽  
Copper Interconnects ◽  
Implicit Time ◽  
Integration Scheme ◽  
Single Element ◽  
Ofhc Copper ◽  
Computation Efficiency ◽  
Backward Euler ◽  
Finite Element Procedure

A finite element procedure using a semi-implicit time-integration scheme has been developed for a cyclic thermoviscoplastic constitutive model for Pb-Sn solder and OFHC copper, two common metallic constituents in electronic packaging applications. The scheme has been implemented in the commercial finite element (FE) code ABAQUS (1995) via the user-defined material subroutine, UMAT. Several single-element simulations are conducted to compare with previous test results, which include monotonic tensile tests, creep tests, and a two-step ratchetting test for 62Sn36Pb2Ag solder; a nonproportional axial-torsional test and a thermomechanical fatigue (TMF) test for OFHC copper. At the constitutive level, we also provide an adaptive time stepping algorithm, which can be used to improve the overall computation efficiency and accuracy especially in large-scale FE analyses. We also compare the computational efforts of fully backward Euler and the proposed methods. The implementation of the FE procedure provides a guideline to apply user-defined material constitutive relations in FE analyses and to perform more sophisticated thermomechanical simulations. Such work can facilitate enhanced understanding thermomechanical reliability issue of solder and copper interconnects in electronic packaging applications.

scholarly journals Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

2012 ◽  
Author(s):  
Kaliappan Jayabal ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Three Dimensional ◽  
Specific Property ◽  
Voronoi Cell ◽  
Polycrystalline Materials ◽  
Element Formulation ◽  
Hybrid Finite Element ◽  
Grain Structures ◽  
Polygonal Elements

Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.

Inclusion of Local Shell Behavior of Tubes Into a Two-Dimensional Beam Approximation of Deformation in Nuclear Fuel Channels

2002 ◽  
Author(s):  
S. Khajehpour ◽  
R. G. Sauve´ ◽  
N. Badie
Keyword(s):  
Finite Element ◽  
Contact Stiffness ◽  
Three Dimensional ◽  
Local Deformation ◽  
Beam Model ◽  
Two Dimensional ◽  
Dimensional Modeling ◽  
Dimensional Finite Element ◽  
Nonlinear Force ◽  
Three Dimensional Finite Element

A method has been developed to incorporate the local three-dimensional shell behavior of two concentric tubes in the two-dimensional beam modeling of the problem. The two dimensional modeling of fuel channels in CANDU pressurized heavy water nuclear reactors is used in lieu of a more accurate three dimensional finite element approach in order to reduce the on-line simulation time which greatly affects the SLAR (Spacer Location And Repositioning) maintenance operation cost during outage. However, effort must be made to include the three-dimensional shell behavior of these channels into the two-dimensional modeling. In recent studies a nonlinear force-dependent model for contact stiffness between the calandria tube and pressure tube has been developed. However, local deformation of calandria the tube at spacer locations due to in-reactor creep leads to settling of the spacer into the calandria tube that consequently reduces the gap between the two tubes. In this work, the effect of local deformation (elastic and creep) of calandria tubes on modeling of contact at spacer locations is assessed using a three dimensional finite element code. The result is incorporated into a two-dimensional beam model of the problem as a reduction in size of the spacers that separate the two tubes. It is shown that the proposed method increases the accuracy of prediction of contact time and the spacer. In general, the method described in this paper suggests a way to incorporate local shell deformation into beam models of slender shell structure.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

scholarly journals Three-Dimensional Response of the Supported-Deep Excavation System: Case Study of a Large Scale Underground Metro Station

Geosciences ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 76
Author(s):  
Ashraf Hefny ◽  
Mohamed Ezzat Al-Atroush ◽  
Mai Abualkhair ◽  
Mariam Juma Alnuaimi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
Deep Excavation ◽  
Metro Station ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The complexities and the economic computational infeasibility associated in some cases, with three-dimensional finite element models, has imposed a motive for many investigators to accept numerical modeling simplification solutions such as assuming two-dimensional (2D) plane strain conditions in simulation of several supported-deep excavation problems, especially for cases with a relatively high aspect ratio in plan dimensions. In this research, a two-dimensional finite element model was established to simulate the behavior of the supporting system of a large-scale deep excavation utilized in the construction of an underground metro station Rod El Farrag project (Egypt). The essential geotechnical engineering properties of soil layers were calculated using results of in-situ and laboratory tests and empirical correlations with SPT-N values. On the other hand, a three-dimensional finite element model was established with the same parameters adopted in the two-dimensional model. Sufficient sensitivity numerical analyses were performed to make the three-dimensional finite element model economically feasible. Results of the two-dimensional model were compared with those obtained from the field measurements and the three-dimensional numerical model. The comparison results showed that 3D high stiffening at the primary walls’ corners and also at the locations of cross walls has a significant effect on both the lateral wall deformations and the neighboring soil vertical settlement.

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