Stress integration procedures for inelastic material models within the Finite Element Method

2002 ◽  
Vol 55 (4) ◽  
pp. 389-414 ◽  
Author(s):  
Milosˇ Kojic´
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Deformation Gradient ◽  
Design And Technology ◽  
Parameter Method ◽  
Material Models ◽  
Mapping Procedure ◽  
Inelastic Material ◽  
Tangent Moduli ◽  
Stress Integration

A review of numerical procedures for stress calculation in the inelastic finite element analysis is presented. The role of stress integration within a time (load) step in the incremental-iterative scheme for the displacements based FE formulation is first given briefly. Then, the basic relations of the explicit algorithms, as the first ones developed in the 70s, are presented. The shortcomings of these algorithms are pointed out. The implicit procedures are presented in some detail, with the emphasis on a general return mapping procedure and the governing parameter method (GPM). Derivation of the consistent tangent moduli represents an important task in the inelastic FE analysis because the overall equilibrium iteration rate depends on these moduli. The basic concepts of this derivation are presented. An important field, very challenging in today’s stage of design and technology, is the large strain deformation of material. A review of the approaches in the large strain domain that includes the rate and the total formulations is given in some detail. Special attention is devoted to the multiplicative decomposition of deformation gradient concept, since that concept is generally favored today. Some unresolved issues, such as the use of the stress and strain measures, are discussed briefly. A number of selected numerical examples illustrate the main topics in the stress integration task, as well as the applications of the stress integration algorithms to various material models. Some concluding remarks and an outline of further research topics are given at the end of the paper. This review article includes 205 references.

scholarly journals Numerical Approximation of Tangent Moduli for Finite Element Implementations of Nonlinear Hyperelastic Material Models

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Wei Sun ◽  
Elliot L. Chaikof ◽  
Marc E. Levenston
Keyword(s):  
Finite Element ◽  
Numerical Approximation ◽  
Structural Model ◽  
Large Strain ◽  
Deformation Gradient ◽  
Mathematical Formulation ◽  
Hyperelastic Material ◽  
Material Models ◽  
Tangent Stiffness Matrix ◽  
Tangent Moduli

Finite element (FE) implementations of nearly incompressible material models often employ decoupled numerical treatments of the dilatational and deviatoric parts of the deformation gradient. This treatment allows the dilatational stiffness to be handled separately to alleviate ill conditioning of the tangent stiffness matrix. However, this can lead to complex formulations of the material tangent moduli that can be difficult to implement or may require custom FE codes, thus limiting their general use. Here we present an approach, based on work by Miehe (Miehe, 1996, “Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large Strain Computational Inelasticity,” Comput. Methods Appl. Mech. Eng., 134, pp. 223–240), for an efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE codes. By perturbing the deformation gradient, the material tangent moduli from the Jaumann rate of the Kirchhoff stress are accurately approximated by a forward difference of the associated Kirchhoff stresses. The merit of this approach is that it produces a concise mathematical formulation that is not dependent on any particular material model. Consequently, once the approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and accuracy of this approach is first demonstrated with a simple neo-Hookean material. Subsequently, a fiber-reinforced structural model is applied to analyze the pressure-diameter curve during blood vessel inflation. Implementation of this approach will facilitate the incorporation of novel hyperelastic material models for a soft tissue behavior into commercial FE software.

Development of Material Constants for Nonlinear Finite-Element Analysis

1988 ◽  
Vol 61 (5) ◽  
pp. 879-891 ◽  
Author(s):  
Robert H. Finney ◽  
Alok Kumar
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Large Strain ◽  
Strain Range ◽  
Nonlinear Finite Element ◽  
Element Analysis ◽  
Material Models ◽  
Tensile Data

Abstract The determination of the material coefficients for Ogden, Mooney-Rivlin, Peng, and Peng-Landel material models using simple ASTM D 412 tensile data is shown to be a manageable task. The application of the various material models are shown to be subject to the type and level of deformation expected, with Ogden showing the best correlation with experimental data over a large strain range for the three types of strain investigated. At low strains, all of the models showed reasonable correlation.

Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem

2018 ◽  
Vol 940 ◽  
pp. 84-88 ◽  
Author(s):  
Kai Oshiro ◽  
Hiroka Miyakubo ◽  
Masaki Fujikawa ◽  
Chobin Makabe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Large Strain ◽  
Deformation Gradient ◽  
Deformation Analysis ◽  
Tetrahedral Elements ◽  
Incompressible Materials ◽  
Smoothed Finite Element Method ◽  
Element Method

A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

On the Study of Distinct Algorithmic Strategies in the Implementation of Advanced Anisotropic Models with Mixed Hardening

2013 ◽  
Vol 554-557 ◽  
pp. 1174-1183 ◽  
Author(s):  
Tiago Jordão Grilo ◽  
Robertt Angelo Fontes Valente ◽  
R.J. Alves de Sousa
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Mapping Procedure ◽  
Anisotropic Models ◽  
Mixed Hardening ◽  
Hardening Law ◽  
Fully Implicit ◽  
Return Mapping ◽  
Multi Stage ◽  
Stress Integration

In this study, suitable distinct stress integration algorithms for advanced anisotropic models with mixed hardening, and their implementation in finite element codes, are discussed. The constitutive model studied in the present work accounts for advanced (non-quadratic) anisotropic yield criteria, namely, the Barlat et al. 2004 model with 18 coefficients (Yld2004-18p), combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex plastic yielding anisotropy and Bauschinger effects, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations.In the present work distinct algorithm classes are analysed: (i) a semi-explicit algorithm that accounts for the sub-incrementation technique; (ii) the cutting-plane approach (semi-implicit integration); and (iii) the fully-implicit multi-stage return mapping procedure, based on the control of the potential residual. The numerical performance of the developed algorithms is inferred by benchmarks in sheet metal forming processes. The quality of the solution is assessed and compared to reference results. In the end, an algorithmic and programming framework is provided, suitable for a direct implementation in commercial Finite Element codes, such as Abaqus (Simulia) and Marc (MSC-Software) packages.

A General Orthotropic von Mises Plasticity Material Model With Mixed Hardening: Model Definition and Implicit Stress Integration Procedure

1996 ◽  
Vol 63 (2) ◽  
pp. 376-382 ◽  
Author(s):  
M. Kojic´ ◽  
N. Grujovic´ ◽  
R. Slavkovic´ ◽  
M. Zˇivkovic´
Keyword(s):  
Equivalent Stress ◽  
Parameter Method ◽  
Plasticity Model ◽  
Integration Procedure ◽  
Mixed Hardening ◽  
Tangent Moduli ◽  
Stress Integration ◽  
Mises Plasticity ◽  
Von Mises ◽  
Von Mises Plasticity

A general orthotropic von Mises plasticity model, with an extension of the Hill’s yield criterion to include mixed hardening, is introduced in the paper. Material constants and equivalent stress-equivalent plastic strain curves are defined in a way to suggest their experimental determination. The model represents a special case of a general anisotropic metal plasticity model proposed by the authors. An implicit stress integration procedure, representing an application of the governing parameter method (GPM) introduced by the first author, is presented. The GPM is briefly described, and the computational procedure, together with calculation of the consistent tangent moduli, are given in some detail for a general three-dimensional deformation, with direction of application to plane stress/shell conditions. Numerical examples illustrate applicability of the model and effectiveness of the computational algorithm.

Hybrid Metal-Composite Interfaces: Aspects of Design, Characterisation, and Simulation

2016 ◽  
Vol 1140 ◽  
pp. 255-263 ◽  
Author(s):  
Robert Kießling ◽  
Franz Hirsch ◽  
Christian Dammann ◽  
Mathias Bobbert ◽  
Markus Pohl ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Simulations ◽  
Connected Components ◽  
Metal Composite ◽  
Cohesive Elements ◽  
Material Models ◽  
Rheological Models ◽  
Suitable Material ◽  
Inelastic Material ◽  
Composite Interfaces

This contribution gives an overview of the simulative engineering of metal-composite interfaces. To this end, several design aspects on the microscale and macroscale are explained and methods to model the mechanical behaviour of the interface within finite element simulations are discussed. This comprises the utilization of cohesive elements with a continuum description of the interface. Likewise, traction-separation based cohesive elements, i.e. a zero-thickness idealization of the interface, are explained and applied to a demonstration example. Within these finite element simulations, the constitutive behaviour of the connected components has to be described by suitable material models. Therefore, inelastic material models are formulated based on rheological models.

Finite Element Analysis for Normal-Temperature Wet Briquetting of Straws

2012 ◽  
Vol 512-515 ◽  
pp. 409-415
Author(s):  
Jian Jun Hu ◽  
Ting Zhou Lei ◽  
Sheng Qiang Shen ◽  
Quan Guo Zhang
Keyword(s):  
Finite Element ◽  
Fossil Fuels ◽  
Large Strain ◽  
Body Movement ◽  
Deformation Gradient ◽  
Computer Software ◽  
Practical Significance ◽  
Gradient Tensor ◽  
Element Analysis ◽  
Balance Principle

As one of important technologies for briquettes production from straws, the normal-temperature wet briquetting technology of straws shows important practical significance in place of fossil fuels that are progressively reduced. According to the characteristics of the normal-temperature wet briquetting of straws having large displacement and large strain, this article provided a finite element calculation method for non-linear straw problems using the large-deformation elastic-plasticity principle. Based on description of straw status by Lagrange method, analyses were performed for deformation gradient tensor, displacement gradient tensor and rigid body movement, and then finite element equations were established for the normal-temperature wet briquetting of straws according to the Green strain, Drucker-Prager criterion and balance principle, providing references for numerical simulation for the normal-temperature wet briquetting of straws with computer software.

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