scholarly journals Development of a continuum plasticity model for the commercial finite element code ABAQUS

2011 ◽  
Vol 2 (2) ◽  
pp. 275-283
Author(s):  
M. Safaei ◽  
W. De Waele
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Euler Method ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Implicit Integration ◽  
Backward Euler ◽  
User Material Subroutine ◽  
Von Mises ◽  
Future Work

The present work relates to the development of computational material models for sheet metalforming simulations. In this specific study, an implicit scheme with consistent Jacobian is used forintegration of large deformation formulation and plane stress elements. As a privilege to the explicitscheme, the implicit integration scheme is unconditionally stable. The backward Euler method is used toupdate trial stress values lying outside the yield surface by correcting them back to the yield surface atevery time increment. In this study, the implicit integration of isotropic hardening with the von Mises yieldcriterion is discussed in detail. In future work it will be implemented into the commercial finite element codeABAQUS by means of a user material subroutine.

Implicit Stress Integration for High-Temperature Inelastic Constitutive Models Using Linearization

2007 ◽  
Vol 340-341 ◽  
pp. 907-912
Author(s):  
Masafumi Akamatsu ◽  
Kazuhiko Nakane ◽  
Nobutada Ohno
Keyword(s):  
High Temperature ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Inelastic Strain ◽  
Euler Method ◽  
Joint Analysis ◽  
Integration Scheme ◽  
Implicit Integration ◽  
Backward Euler

In this study, a linearization approach is used to develop an implicit integration scheme for high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments.

Explicit and Implicit Integration Algorithms for an Elastoplastic Pipe-Soil Interaction Macroelement Model

2008 ◽  
Author(s):  
Yinghui Tian ◽  
Mark J. Cassidy
Keyword(s):  
Yield Surface ◽  
Nodal Point ◽  
Elastic Behaviour ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Implicit Integration ◽  
Soil System ◽  
Total Displacement ◽  
Integration Algorithms

This paper presents the numerical formulation of an elastoplastic force-resultant model to numerically simulate the interaction of a pipe with the soil. This approach, which accounts for the load-displacement behaviour of the pipe-soil system on a macroelement level, is becoming increasingly popular in offshore engineering. The model consists of a yield surface, a non-associated flow rule, an isotropic hardening law and a description of purely elastic behaviour. It can be used to predict the behavior of one segment of pipe or numerous models can be attached to structural finite elements as nodal point elements. The latter allows the practical analysis of long pipelines. Further, by removing a number of macroelements from the pipeline, the effect of free span can be studied. To numerically incorporate large numbers of macroelements into a structural analysis, efficient and robust integration algorithms are essential. The use of both explicit and implicit integration algorithms are explored in this paper. In the explicit algorithm, the Euler forward integration scheme is adopted to achieve the real force state incrementally for each substep. On the other hand, the Euler backward integration scheme is adopted in the implicit algorithm. In this case the load state is iteratively “returned” back to the yield surface according to the end of the total displacement increment. Illustrative calculation examples are provided in this paper to demonstrate and compare the performance of the suggested algorithms.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

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.

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.

Densification Behavior of Metal Powder Under Uniaxial Cold Compaction

2010 ◽  
Author(s):  
Mostafa Darroudi ◽  
Hojat Ghassemi ◽  
Mahmoud Akbari Baseri
Keyword(s):  
Finite Element ◽  
Metal Powder ◽  
Volume Fraction ◽  
Compaction Pressure ◽  
Solid Volume Fraction ◽  
Powder Compaction ◽  
Wall Friction ◽  
Isotropic Hardening ◽  
Spherical Powder ◽  
Von Mises

Metal powder compaction is a quite important process in Powder Metallurgy (PM) industry and it is widely applied in the manufacturing of key components in different fields. During metal powder compaction, the solid volume fraction changes and many mechanical characteristics become different. The Finite Element simulation provides a flexible and efficient approach for the researches of this process and its complicated mechanical behaviors. In this paper, several 2D finite element spherical powder compaction models are generated. Different particle arrangements are build up and different friction coefficients are set to the inter-particle contacts and die wall contact for a certain arrangement. The Von Mises yield surface with isotropic hardening plasticity model is applied in the simulation and the displacement controlled load is used to compress the structure up to 25% of die height. Results show that the die wall friction increases compaction pressure but inter-particle friction has negligible effect.

FINITE ELEMENT IMPLEMENTATION OF A SUPER-ELASTIC CONSTITUTIVE MODEL FOR TRANSFORMATION RATCHETTING OF NiTi ALLOY

2012 ◽  
Vol 09 (01) ◽  
pp. 1240022 ◽  
Author(s):  
Q. H. KAN ◽  
G. Z. KANG ◽  
S. J. GUO
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Niti Alloy ◽  
Cyclic Stress ◽  
Euler Method ◽  
Convergence Criterion ◽  
Integration Algorithm ◽  
Finite Element Implementation ◽  
Backward Euler ◽  
Forward Transformation

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.

Modeling of the Long-Term Behavior of Glassy Polymers

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Sami Holopainen ◽  
Mathias Wallin
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Glassy Polymers ◽  
Integration Scheme ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Plastic Spin ◽  
Backward Euler ◽  
Long Term Behavior

The constitutive model for glassy polymers proposed by Arruda and Boyce (BPA model) is reviewed and compared to experimental data for long-term loading. The BPA model has previously been shown to capture monotonic loading accurately, but for unloading and long-term behavior, the response of the BPA model is found to deviate from experimental data. In the present paper, we suggest an efficient extension that significantly improves the predictive capability of the BPA model during unloading and long-term recovery. The new, extended BPA model (EBPA model) is calibrated to experimental data of polycarbonate (PC) in various loading–unloading situations and deformation states. The numerical treatment of the BPA model associated with the finite element analysis is also discussed. As a consequence of the anisotropic hardening, the plastic spin enters the model. In order to handle the plastic spin in a finite element formulation, an algorithmic plastic spin is introduced. In conjunction with the backward Euler integration scheme use of the algorithmic plastic spin leads to a set of algebraic equations that provides the updated state. Numerical examples reveal that the proposed numerical algorithm is robust and well suited for finite element simulations.

Three-dimensional elastic-plastic damage constitutive model of wood

Holzforschung ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Lipeng Zhang ◽  
Qifang Xie ◽  
Baozhuang Zhang ◽  
Long Wang ◽  
Jitao Yao
Keyword(s):  
Constitutive Model ◽  
Damage Mechanics ◽  
Euler Method ◽  
Isotropic Hardening ◽  
Damage Initiation ◽  
Elastic Plastic ◽  
Plastic Damage ◽  
Backward Euler ◽  
Tension And Compression ◽  
Damage Constitutive Model

AbstractA 3D combined elastic-plastic damage constitutive model for wood is proposed within the theoretical framework of classical plasticity and continuum damage mechanics (CDM). The model is able to describe the various behavior of wood under loading, including the orthotropic elasticity, strengths inequality under tension and compression in each orthotropic direction, ductile softening under longitudinal compression, brittle failure under transverse tension, and parallel shearing, densification hardening under transverse compression. Hoffman criterion and a set of eight separate failure criteria were used to define wood yielding and damage initiation, respectively. Isotropic hardening was assumed after yielding and defined by an exponential type function. The constitutive model was implicitly discretized using backward Euler method, solved through the return mapping algorithm and implemented into ABAQUS through the user-defined material subroutine (UMAT). The proposed model was firstly verified by material property tests considering different stress states: monotonic and repeated tension and compression (in both parallel and perpendicular-to-grain directions), parallel-to-grain shearing, and the interactions between perpendicular-to-grain compression/tension and parallel-to-grain shearing, etc. Mechanical behavior of typical structural elements was further simulated to validate the proposed constitutive model.

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