An unsymmetric 8‐node plane element immune to mesh distortion for linear isotropic hardening material

2021 ◽  
Author(s):  
Xiaotian Chen ◽  
Wei Chen ◽  
Jiangping Xu ◽  
Wenbin Tu ◽  
Sellakkutti Rajendran ◽  
...  
Keyword(s):  
Isotropic Hardening ◽  
Mesh Distortion ◽  
Hardening Material ◽  
Plane Element

Study the Non-Linear Heat-Elasto-Plastic Constitutive Relation

2011 ◽  
Vol 415-417 ◽  
pp. 2130-2133 ◽  
Author(s):  
Xiao Jiu Feng ◽  
Li Fu Liang ◽  
Si Yuan Wang
Keyword(s):  
Constitutive Relation ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Torsion Test ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
Incremental Theory ◽  
Loading Function ◽  
Testing Data ◽  
Strain Space

This paper adopts Macroscopic Phenomenological Method to establish constitutive relation. In order to maintain better approximation, it adopts testing data of typical stress path, testing data of uniaxial tension and torsion test. Applying multidimensional incremental theory under general loading law, on the base of certain loading function of stress space and loading function of strain space, this essay drives heat-elasto-plastic constitutive relation of heated isotropic hardening material under the condition of elasto-plastic decoupling. Meanwhile, this constitutive relation also suits for kinematic hardening material and elastic-perfectly plastic material. This paper builds a means of driving constitutive relation of multidimensional incremental theory under general loading law in strain space.

SOLVABILITY OF A QUASI-STEADY ROLLING PROBLEM WITH SLIGHTLY COMPRESSIBLE MATERIAL MODEL

2007 ◽  
Vol 04 (02) ◽  
pp. 335-351 ◽  
Author(s):  
T. A. ANGELOV
Keyword(s):  
Material Model ◽  
Equivalent Strain ◽  
Linearization Method ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
Existence And Uniqueness Results ◽  
Slightly Compressible ◽  
Uniqueness Results ◽  
Method Of Solution ◽  
Successive Linearization Method

A quasi-steady rolling problem with slightly compressible, rigid-viscoplastic and isotropic hardening material model and nonlinear Coulomb friction law are studied. The problem is stated in the form of a nonlinear variational inequality coupled with an equivalent strain evolution equation. Under restrictions on the material characteristics, existence and uniqueness results are obtained and the convergence of a successive linearization method of solution is proved. An algorithm, combining this method with the finite element method, is proposed and applied to solve numerically an example problem.

Quasi-statically growing crack tip fields in plastically compressible hardening-softening-hardening solid

2018 ◽  
Vol 9 (4) ◽  
pp. 532-547 ◽  
Author(s):  
Sushant Singh ◽  
Debashis Khan
Keyword(s):  
Constitutive Relation ◽  
Numerical Study ◽  
Crack Tip ◽  
Small Scale ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Hardening Material ◽  
Static Mode ◽  
Content Type ◽  
Crack Tip Fields

Purpose As the normality concept for frictional dilatant material has a serious drawback, the key feature in this numerical study is that the material here is characterized by elastic-viscoplastic constitutive relation with plastic non-normality effect for two different hardness functions. The paper aims to discuss this issue. Design/methodology/approach Quasi-static, mode I plane strain crack tip fields have been investigated for a plastically compressible isotropic hardening–softening–hardening material under small-scale yielding conditions. Finite deformation, finite element calculations are carried out in front of the crack with a blunt notch. For comparison purpose a few results of a hardening material are also provided. Findings The present numerical calculations show that crack tip deformation and the field quantities near the tip significantly depend on the combination of plastic compressibility and slope of the hardness function. Furthermore, the consideration of plastic non-normality flow rule makes the crack tip deformation as well as the field quantities significantly different as compared to those results when the constitutive equation exhibits plastic normality. Originality/value To the best of the authors’ knowledge, analyses, related to the constitutive relation exhibiting plastic non-normality in the context of plastic compressibility and softening (or softening hardening) on the near tip fields, are not explored in the literature.

An Assessment of Kinematic Hardening Thermal Ratcheting

1974 ◽  
Vol 96 (3) ◽  
pp. 214-221 ◽  
Author(s):  
T. M. Mulcahy
Keyword(s):  
Thermal Loading ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Strain Accumulation ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Thermal Ratcheting

Analytical comparisons are made between the thermal ratcheting response of a kinematic hardening material, a perfectly plastic, and an isotropic hardening material for a two-element assembly. Significant differences were found in the range of mechanical and thermal loading for which ratcheting occurred and the magnitude of the strain accumulation when ratcheting did occur. The kinematic hardening strain accumulation predicted was always smallest.

Simplified Equations for Predicting Secondary Stress Around Pipe’s Circumference

2013 ◽  
Author(s):  
Junkan Wang ◽  
Rajil Saraswat ◽  
Ali Mirzaee-Sisan
Keyword(s):  
Residual Stress ◽  
Plastic Material ◽  
Axial Strain ◽  
Quadratic Equation ◽  
Material Behavior ◽  
Global Maximum ◽  
Isotropic Hardening ◽  
Element Analysis ◽  
Hardening Material ◽  
Maximum Residual Stress

This paper examines the magnitude and location of the maximum residual stress induced in pipes after the process of bending, reverse-bending and straightening. Dimensional analysis is used to establish generalized equations relating the maximum residual stress magnitude and location to the pipe geometry, maximum bending curvature and pipe material’s yield stress. 64 design cases based on an analytical solution assuming elastic-perfectly-plastic material behavior have been conducted. Regression analysis has revealed that the magnitude of the maximum residual stress can be conservatively approximated by a simplified quadratic equation involving the maximum axial bending strain, whereas the location of the maximum residual stress can be approximated by a linear function based on the same. Both equations are expected to be valid and conservative for X65 and X70 grade steel pipes under global maximum axial strain between 1% and 3%. Non-linear finite element analysis based on a realistic design example with isotropic hardening material is used to validate the prediction results based on the simplified equations.

Strain Hardening Analysis Coupled to Remeshing Procedure Application to Sheet Hydroforming Processes

2011 ◽  
Vol 418-420 ◽  
pp. 1255-1258
Author(s):  
Slimani Faouzi ◽  
Abel Cherouat ◽  
A. Ayadi ◽  
Mohamed Ali Rezgui
Keyword(s):  
Mesh Generation ◽  
Thin Sheet ◽  
Irreversible Processes ◽  
Isotropic Hardening ◽  
Global Measure ◽  
Mesh Distortion ◽  
Sheet Hydroforming ◽  
Computational Environment ◽  
Displacement Thickness ◽  
Automatic Mesh

In this study, we present an experimental/numerical methodology which aims to improve 3D thin sheet hydroforming considering coupled constitutive equations formulated in the framework of of irreversible processes accounting for isotropic hardening as well as isotropic ductile damage. The experimental study is dedicated to the identification of stress-strain flow from the global measure of pole displacement, thickness evolution and internal pressure expansion. Or during the hydroforming processes severe mesh distortion of element occur after a few incremental steps. Hence an automatic mesh generation with remeshing capabilities is essential to carry out the FEA. The proposed technique based on geometrical criteria includes adaptive refinement and coarsening procedure is integrated in a computational environment.

On the Influence of Hardening and Anisotropy on the Plane-Strain Compression of Thin Metal Strip

1977 ◽  
Vol 44 (2) ◽  
pp. 271-278 ◽  
Author(s):  
I. F. Collins ◽  
S. A. Meguid
Keyword(s):  
Yield Criterion ◽  
Metal Strip ◽  
Thin Metal ◽  
Isotropic Hardening ◽  
Strain History ◽  
Anisotropic Hardening ◽  
Hardening Material ◽  
Static Compression ◽  
Perfectly Plastic ◽  
Quasi Static Compression

This paper presents a theoretical investigation into the continued quasi-static compression of a thin metal strip between two rigid, parallel rough dies. Three different constitutive postulates for the strip material are considered: (a) rigid isotropic hardening, (b) rigid-perfectly plastic with an anisotropic yield criterion, and (c) rigid-kinematic (anisotropic) hardening. An initially homogeneous such strip develops inhomogeneities through its thickness as it is compressed. This is due to the dependence of the yield locus on the rigid-body spin for an anisotropic material and on the strain-history for a hardening material. The length of the dies is supposed to be much greater than the current strip thickness. The solution is hence effectively independent of position along the length of the strip and can be found by integrating an ordinary differential equation.

Biaxial Plastic Simple Waves With Combined Kinematic and Isotropic Hardening

1970 ◽  
Vol 37 (4) ◽  
pp. 1100-1106 ◽  
Author(s):  
R. P. Goel ◽  
L. E. Malvern
Keyword(s):  
Wave Speed ◽  
Cylindrical Tube ◽  
Simple Wave ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
One Dimensional ◽  
Shear Wave Speed ◽  
Simple Waves ◽  
Thin Walled ◽  
Elastic Shear

The study of one-dimensional combined longitudinal and torsional plastic wave propagation in a thin-walled cylindrical tube of isotropic-hardening material was first carried out by Clifton. In this paper, the same problem is studied for a combined kinematic and isotropic hardening material. Simple wave solutions are obtained. In some cases, a discontinuity in shear stress occurs, propagating at the elastic shear-wave speed c2, followed by a slow plastic simple wave.

Higher-order assumed strain plane element immune to mesh distortion

2020 ◽  
Vol 37 (9) ◽  
pp. 2957-2981 ◽  
Author(s):  
Mohammad Rezaiee-Pajand ◽  
Nima Gharaei-Moghaddam ◽  
Mohammadreza Ramezani
Keyword(s):  
Degrees Of Freedom ◽  
Triangular Element ◽  
Mesh Distortion ◽  
Content Type ◽  
Assumed Strain ◽  
Plane Element ◽  
Displacement Based ◽  
Locking Phenomena ◽  
Assumed Strain Method ◽  
Better Than

Purpose This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

Sign in / Sign up

Export Citation Format

Share Document