scholarly journals A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteri

2021 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
navab hosseini
Keyword(s):  
Finite Element ◽  
Numerical Approximation ◽  
Constitutive Models ◽  
Yield Function ◽  
Computational Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Plane Strain Tension ◽  
Stress Integration ◽  
Cylindrical Cup

In this paper, we have modi?ed the stress integration scheme proposed by Choi and Yoon (2019), which is based on the numerical approximation of the yield function gradients, to implement in the ?nite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p (Barlat et al., 2005), CPB06ex2 (Plunkett et al., 2008) and Yld2011-27p (Aretz and Barlat, 2013) criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon (2019), and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the ?finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.

Implicit Stress Integration and Consistent Tangent Matrix for Yoshida’s 6th Order Polynomial Yield Function Combined with Yoshida-Uemori Kinematic Hardening Rule

2015 ◽  
Vol 651-653 ◽  
pp. 558-563 ◽  
Author(s):  
Hiroshi Hamasaki ◽  
Fusahito Yoshida ◽  
Takeshi Uemori
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Equivalent Plastic Strain ◽  
Yield Function ◽  
Alloy Sheet ◽  
Integration Scheme ◽  
State Variables ◽  
Tangent Matrix ◽  
Fully Implicit ◽  
Stress Integration

This paper describes fully implicit stress integration scheme for Yoshida’s 6thorder yield function combined with Yoshida-Uemori kinematic hardening model and its consistent tangent matrix. Cutting plane method was employed for accurate integrations of stress and state variables appeared in Yoshida-Uemori model. In the present scheme, equivalent plastic strain, stress tensor and all the state variables are treated as independent variables in order to handle the 6th order yield function which is not the J2 yield function, and the equilibriums for each variables are solved for the stress integration. Subsequently, exact consistent tangent matrix which is necessary for implicit static finite element simulation was obtained. The proposed scheme was implemented into finite element code LS-DYNA and deep drawing process for aluminum alloy sheet was calculated. The earing appearance after drawing was compared with the experiment.

Cazacu and Barlat Criterion Identification Using the Cylindrical Cup Deep Drawing Test and the Coupled Artificial Neural Networks – Genetic Algorithm Method

2012 ◽  
Vol 504-506 ◽  
pp. 637-642 ◽  
Author(s):  
Hamdi Aguir ◽  
J.L. Alves ◽  
M.C. Oliveira ◽  
L.F. Menezes ◽  
Hedi BelHadjSalah
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Deep Drawing ◽  
Inverse Analysis ◽  
Computational Time ◽  
Ann Model ◽  
Drawing Test ◽  
Artificial Neural ◽  
Deep Drawing Test ◽  
Cylindrical Cup

This paper deals with the identification of the anisotropic parameters using an inverse strategy. In the classical inverse methods, the inverse analysis is generally coupled with a finite element code, which leads to a long computational time. In this work an inverse analysis strategy coupled with an artificial neural network (ANN) model is proposed. This method has the advantage of being faster than the classical one. To test and validate the proposed approach an experimental cylindrical cup deep drawing test is used in order to identify the orthotropic material behaviour. The ANN model is trained by finite element simulations of this experimental test. To reduce the gap between the experimental responses and the numerical ones, the proposed method is coupled with an optimization procedure based on the genetic algorithm (GA) to identify the Cazacu and Barlat’2001 material parameters of a standard mild steel DC06.

Improving finite element results in modeling heart valve mechanics

2018 ◽  
Vol 232 (7) ◽  
pp. 718-725 ◽  
Author(s):  
Emily Earl ◽  
Hadi Mohammadi
Keyword(s):  
Finite Element ◽  
Heart Valve ◽  
Numerical Technique ◽  
Strain Tensor ◽  
Computational Cost ◽  
Constitutive Models ◽  
Least Square ◽  
Computational Time ◽  
Finite Element Models ◽  
Fine Mesh

Finite element analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available finite element models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive finite element models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh finite element models to provide accuracy comparable to that of fine mesh finite element models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the finite difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the finite element mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial finite element packages such as ANSYS and/or ABAQUS.

Comparison of Three-Dimensional Shape Memory Alloy Constitutive Models: Finite Element Analysis of Actuation and Superelastic Responses of a Shape Memory Alloy Tube

2013 ◽  
Author(s):  
Pingping Zhu ◽  
L. Catherine Brinson ◽  
Edwin Peraza-Hernandez ◽  
Darren Hartl ◽  
Aaron Stebner
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Benchmark Problems ◽  
Internal Variables ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Analysis And Design

Many three-dimensional constitutive models have been proposed to enhance the analysis and design of shape memory alloy (SMA) structural components. Phenomenological models are desirable for this purpose since they describe macroscopic responses using internal variables to govern the homogenized material response. Because they are computationally efficient on the scale of millimeters to meters, these models are often the only viable option when assessing the response of full-scale SMA components for engineering applications. Thus, many different 3D SMA constitutive models have been developed. However, for their intended user, the application engineer, a clear and straightforward methodology has not been established for selecting a model to use in a design process. A primary goal of the Consortium for the Advancement of Shape Memory Alloy Research and Technology (CASMART) modeling working group has been establishment of model selection methodology. One critical step in this process is the development of benchmark problems that clearly illustrate the capabilities and efficiencies of models. In this paper, we propose a set of benchmark problems centered on an SMA tube component. These problems have been selected to demonstrate both uniaxial and multiaxial, actuation and superelastic capabilities of 3D SMA models. We then use finite element simulations of these benchmark problems to compare and contrast both the material modeling and implementation of three unique SMA constitutive models.

A Finite-Element Based Framework for Transient Rotor Dynamic Simulations

2020 ◽  
Author(s):  
Anurag Rajagopal ◽  
Dilip K. Mandal
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Integration Scheme ◽  
Test Case ◽  
Computationally Efficient ◽  
Time Step ◽  
Dynamic Simulations ◽  
Adaptive Time Step ◽  
Time Integration Scheme ◽  
Rotor Dynamic

Abstract Transient simulations play a key role in the analysis and subsequent design of structural components with one or more rotating parts. A framework is proposed to this effect, centered around the finite-element solver OptiStruct, consisting of a time integration scheme built on the Newmark family with an appropriate adaptive time-step control. The process accounts for a computationally efficient handling of nonlinearities that might arise through bearings and casings. This solution is detailed starting from the governing equations for transient rotor dynamics to the nuances of the time marching scheme, and this process is applied to a test case from which conclusions are drawn that might be of interest to practicing engineers. These conclusions include insights into enforced motion, operation at or near critical speeds, rotor damping and contact. This work is aimed at producing a user-friendly and robust tool and process for the practicing engineer to perform complex rotor dynamic analysis.

Modelling Recrystallisation during Thermomechanical Processing Using CAFE

2004 ◽  
Vol 467-470 ◽  
pp. 623-628 ◽  
Author(s):  
S. Das ◽  
Eric J. Palmiere ◽  
I.C. Howard
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cellular Automata ◽  
Thermomechanical Processing ◽  
Constitutive Models ◽  
Computational Time ◽  
Physical Sciences ◽  
Element Mesh ◽  
Dislocation Densities ◽  
Macro Scale

A common feature that stimulates modelling efforts across the various physical sciences is that complex microscopic behaviour underlies apparently simple macroscopic effects. Mathematical formulations attempt to capture the initial and evolving microstructural entities either implicitly or explicitly and link their effects to measurable macroscopic variables such as load or stress by averaging out any microscopic fluctuations. The implicit formulations that ignore the inherent spatial heterogeneity in the deforming domain form the basis of constitutive models for input to finite element (FE) systems. On the other hand, explicit formulations to capture and link microstructural entities rely on narrowing down the size of each finite element, thereby increasing the number of finite elements in the deforming domain, an effect accompanied by a rapid growth in computational time. The model described here, Cellular Automata based Finite Elements (CAFE), utilises the Cellular Automata technique to represent initial and evolving microstructural features (e.g., dislocation densities, grain sizes, etc.) in C-Mn steels at an appropriate length scale by linking the macro-scale process variables obtained using an overlying finite element mesh. Differences will be illustrated between single and two-pass hot rolling experiments.

Multiple Grid and Multiple Time-Scale (MGMT) Simulations in Continuum Mechanics

2012 ◽  
Author(s):  
Tejas Ruparel ◽  
Azim Eskandarian ◽  
James Lee
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Time Scale ◽  
Computational Time ◽  
Discrete Equation ◽  
Integration Scheme ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Time Step ◽  
Stable Algorithm

The work presented in this paper describes a general formulation for implementation of Multiple Grid and Multiple Time-scale (MGMT) simulations in continuum mechanics. Using this method one can solve problems in structural dynamics in which the domain under consideration can be selectively discretized (spatially and temporally) in critical and remote regions, hence allowing the user to obtain a desired level of accuracy and save computational time. The formulation is based upon the fundamental principles of Domain Decomposition Methods (DDM) used to obtain the semi-discrete equation of motion for coupled sub-domains augmented with interface energy. Lagrange Multipliers, based on Schur’s dual formulation, are used to enforce interface conditions since they not only ensure energy balance but also enforce continuity of kinematic quantities across the interface. The Finite Element Tearing and Interconnecting (FETI) based Multi Time-step (MTS) coupling algorithm proposed by Prakash and Hjelmstad [1] is then used to obtain the evolution of unknown quantities in respective sub-domains using different time-steps and/or different variants of the Newmark Implicit Method. Our work is in the direction of coupling this MTS algorithm with multiple grid discretizations in respective subdomains. We propose using coarse grid discretization to define the mortar space between non-conforming sub-domains and show that this particular choice when combined with the implicit integration scheme yields a stable algorithm for MGMT simulations. The formulation is implemented, comprehensively, using Finite Element Methods and programming in FORTRAN 90. Several scenarios with different mesh densities and time-steps are evaluated to analyze the efficiency of MGMT simulations. The purpose of this paper is to study and evaluate its accuracy and stability by looking at evolution and distribution of quantities across the connecting interface. Results show that the interface coupling for non-conforming sub-domains with distinct integration time-steps can be efficiently modeled using this approach.

scholarly journals An efficient and robust VUMAT implementation of elastoplastic constitutive laws in Abaqus/Explicit finite element code

2018 ◽  
Vol 19 (3) ◽  
pp. 308 ◽  
Author(s):  
Lu Ming ◽  
Olivier Pantalé
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Computational Time ◽  
Plastic Strain Rate ◽  
Integration Scheme ◽  
Elastoplastic Material ◽  
Finite Element Software ◽  
Return Mapping

This paper describes the development of an efficient and robust numerical algorithm for the implementation of elastoplastic constitutive laws in the commercial non-linear finite element software Abaqus/Explicit through a VUMAT FORTRAN subroutine. In the present paper, while the Abaqus/Explicit uses an explicit time integration scheme, the implicit radial return mapping algorithm is used to compute the plastic strain, the plastic strain rate and the temperature at the end of each increment instead of the widely used forward Euler approach. This more complex process allows us to obtain more precise results with only a slight increase of the total computational time. Corrector term of the radial return scheme is obtained through the implementation of a safe and robust Newton–Raphson algorithm able to converge even when the piecewise defined hardening curve is not derivable everywhere. The complete method of how to implement a user-defined elastoplastic material model using the radial return mapping integration scheme is presented in details with the application to the widely used Johnson–Cook constitutive law. Five benchmark tests including one element tests, necking of a circular bar and 2D and 3D Taylor impact tests show the efficiency and robustness of the proposed algorithm and confirm the improved efficiency in terms of precision, stability and solution CPU time. Finally, three alternative constitutive laws (the TANH, modified TANH and Bäker laws) are presented, implemented through our VUMAT routine and tested.

Development of a finite element neck model for head-first compressive impacts: Toward the assessment of motorcycle neck protective equipment

2021 ◽  
pp. 095441192110181
Author(s):  
Mohammad Nasim ◽  
Alessandro Cernicchi ◽  
Ugo Galvanetto
Keyword(s):  
Finite Element ◽  
Injury Risk ◽  
Constitutive Models ◽  
Assessment Process ◽  
Protective Equipment ◽  
Computationally Efficient ◽  
Flexion Extension ◽  
Hybrid Iii ◽  
The Mean ◽  
Motorcycle Crashes

Head-first compressive impacts occur in motorcycle crashes and may result in serious to fatal neck injuries to riders. Equipment to protect the riders’ necks from these injuries are available in the market; however, their effectiveness in reducing injury risk is not clear, either due to the lack of scientific evidences or assessment with any prevalently accepted standard. This paper presents a finite element ligamentous neck model, developed as a computationally efficient tool, for future use in the computational phase of assessment process of neck protective equipment. The 3D cervical spine was generated using the mean statistical dimensions of vertebrae and proposed constitutive models, provided in the scientific literature. Ligaments, for the vertebra-vertebra and Hybrid III head–vertebra ligamentous joints, were introduced with the aid of published anatomical descriptions. For validation, the response of the head-neck system under compressive loadings and the flexion-extension bending stiffness of the neck at the segment level were compared against experimental data. The advanced CORrelation and Analysis (CORA) algorithm was applied on the validation responses to assess biofidelity of the model. The results indicate that the model is functional and meets ISO/TR9790 standard as a “good” biofidelic model.

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