Constitutive Law of Finite Deformation Elastoplasticity With Proportional Loadings

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
H. Darijani ◽  
R. Naghdabadi
Keyword(s):  
Constitutive Equation ◽  
Finite Deformation ◽  
Constitutive Models ◽  
Pressure Vessels ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Proportional Loading ◽  
Von Mises ◽  
Plastic Parts

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite deformation elastoplasticity.

A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations

2001 ◽  
Vol 74 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Jeffrey E. Bischoff ◽  
Ellen M. Arruda ◽  
Karl Grosh
Keyword(s):  
Uniaxial Tension ◽  
Volume Change ◽  
Constitutive Models ◽  
Hydrostatic Compression ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Volume Response ◽  
Using Data ◽  
Nonlinear Elastic

Abstract Although traditional constitutive models for rubbery elastic materials are incompressible, many materials that demonstrate nonlinear elastic behavior are somewhat compressible. Clearly important in hydrostatic deformations, compressibility can also significantly affect the response of elastomers in applications for which several boundaries are rigidly fixed, such as bushings, or triaxial states of stress are realized. Compressibility is also important for convergence of finite element simulations in which a rubbery elastic constitutive law is in use. Volume changes that reflect compressibility have been observed historically in both uniaxial tension and hydrostatic compression tests; however, there appear to be no data obtained from both types of tests on the same material by which to validate a compressible hyperelastic law. In this paper, we propose a new compressible hyperelastic constitutive law for elastomers and other rubbery materials in which entropy and internal energy changes contribute to the volume change. Using data from the literature, we show that this law is capable of reproducing both the pressure—volume response of elastomers in hydrostatic compression, as well as the stress—stretch and volume change—stretch data of elastomers in uniaxial tension.

Nonlinear Constitutive Models and the Finite Element Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Luis G. Maqueda ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Constitutive Law ◽  
Elastic Behavior ◽  
Deformation Analysis ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Nonlinear Constitutive Models ◽  
Nonlinear Elastic

In this investigation, the use of three different nonlinear constitutive models based on the hyper-elasticity theory with the absolute nodal coordinate formulation is considered. These three nonlinear constitutive models are based on the Neo-Hookean constitutive law for compressible materials, the Neo-Hookean constitutive law for incompressible materials, and the Mooney-Rivlin constitutive law in which the material is assumed to be incompressible. These models, which allow capturing Poisson modes, are suitable for many materials and applications, including rubber-like materials and biological tissues which are governed by nonlinear elastic behavior and are considered incompressible or nearly incompressible. Numerical examples that demonstrate the implementation of these nonlinear constitutive models in the absolute nodal coordinate formulation are presented. The results obtained using the nonlinear and linear constitutive models are compared in this study. The results show that when linear constitutive models are used in the large deformation analysis, singular configurations are encountered and basic formulas such as Nanson’s formula are no longer valid. These singular deformation configurations are not encountered when the nonlinear constitutive models are used.

Application of a Smooth Approximation of the Schmid's Law to a Single Crystal Gas Turbine Blade

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Alessandro D. Ramaglia
Keyword(s):  
Single Crystal ◽  
Constitutive Models ◽  
Material Model ◽  
Research Literature ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Full Potential ◽  
Smooth Approximation ◽  
Suitable Material ◽  
Von Mises

In industrial practice the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost, and time for the minimum testing campaign necessary to identify the model and preexisting standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modeled is isotropic, commercial finite element (FE) packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based superalloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate, and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behavior. In what follows this problem is addressed by showing how single crystal plasticity modeling can be reduced to the adoption of an anisotropic elastic behavior with a sort of von Mises yield surface.

Thermal Ratcheting With Kinematic Hardening in a Two-Bar Assembly With Unequal Areas and Properties

1976 ◽  
Vol 98 (3) ◽  
pp. 256-263 ◽  
Author(s):  
A. R. Brunsvold ◽  
H. U. Ahmed ◽  
C. C. Stone
Keyword(s):  
Kinematic Hardening ◽  
Pressure Vessels ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Thermal Loads ◽  
Strain Behavior ◽  
Thermal Ratcheting ◽  
Cyclic Changes ◽  
Inelastic Strains ◽  
Special Case

An analytical model based on a two-bar assembly with unequal areas and material properties is used to determine inelastic stress-strain behavior under a steady mean load and cyclic thermal loads. The study with the model extends previous study on thermal ratcheting with kinematic hardening. The model exhibits much of the behavior of interest in design of pressure vessels subject to thermal loads: elastic behavior, shakedown, ratcheting, captive plastic behavior (a special case of elastic followup), and plastic cycling. The expressions for cyclic changes in stress and cyclic inelastic strains are developed, and the mean-load and thermal-load bounds for the behavior modes are mapped.

Stress Field Around a Large Opening in a Pressure Vessel During a Major Repair

2009 ◽  
Author(s):  
Erik Garrido ◽  
Euro Casanova
Keyword(s):  
Pressure Vessel ◽  
New Technologies ◽  
Mechanical Design ◽  
General Purpose ◽  
Pressure Vessels ◽  
Mechanical Equipment ◽  
Stress Distributions ◽  
Large Opening ◽  
Von Mises ◽  
Case Basis

It is a regular practice in the oil industry to modify mechanical equipment to incorporate new technologies and to optimize production. In the case of pressure vessels, it is occasionally required to cut large openings in their walls in order to have access to the interior part of the equipment for executing modifications. This cutting process produces temporary loads, which were obviously not considered in the original mechanical design. Up to now, there is not a general purpose specification for approaching the assessments of stress levels once a large opening in a vertical pressure vessel has been made. Therefore stress distributions around large openings are analyzed on a case-by-case basis without a reference scheme. This work studies the distribution of the von Mises equivalent stresses around a large opening in FCC Regenerators during internal cyclone replacement, which is a frequently required practice for this kind of equipment. A finite element parametric model was developed in ANSYS, and both numerical results and illustrating figures are presented.

scholarly journals Investigating friction spin welding of thermoplastics in shear joint configuration

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Tarun Bindal ◽  
Ravindra K. Saxena ◽  
Sunil Pandey
Keyword(s):  
Joint Strength ◽  
Rotational Velocity ◽  
Pressure Vessels ◽  
Frictional Heat ◽  
Hydraulic Pressure ◽  
Joint Configuration ◽  
Burst Test ◽  
Shear Joint ◽  
Plastic Parts ◽  
Welding Pressure

AbstractThe welding of thermoplastic pipes under a shear joint configuration using friction spin welding is investigated. The shear joint configuration consists of two cylindrical and concentric polypropylene plastic parts joined with each other at their interfacing cylindrical surfaces through frictional heat generation. The effects of welding pressure and rotational velocity on the joint overlap distance and joint strength between the parts of polypropylene plastic are evaluated. The study is of a specific application in making plastic pressure vessels and joining of pipes. The joint strength is tested by conducting the hydraulic pressure burst test. The burst test is conducted for welded specimens manufactured using different values of rotational velocity and welding pressure. It is observed that at the constant spin velocities, the welding pressure in the range 64.8 to 65.2 kPa produced better joint strength than the other values of welding pressure in the overall range 64–76 kPa. It is concluded that the suitable welding pressure range to manufacture polypropylene plastic pressure vessels in the shear joint configuration using friction spin welding is 64.5 to 65.2 kPa. Further, it is established that the user can control the joint overlap distance at 64.8 kPa welding pressure by selectively controlling the rotational velocity in the range of 700 to 2500 rpm.

scholarly journals 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

An Analysis of Filament Overwound Toroidal Pressure Vessels and Optimum Design of Such Structures

2002 ◽  
Vol 124 (2) ◽  
pp. 215-222 ◽  
Author(s):  
Shuguang Li ◽  
John Cook
Keyword(s):  
Optimum Design ◽  
Equivalent Stress ◽  
Mechanical Damage ◽  
Stress Rupture ◽  
Optimization Procedure ◽  
Pressure Vessels ◽  
Thickness Variation ◽  
Von Mises Equivalent Stress ◽  
Metal Liner ◽  
Von Mises

This paper is concerned with the membrane shell analysis of filament overwound toroidal pressure vessels and optimum design of such pressure vessels using the results of the analysis by means of mathematical nonlinear programming. The nature of the coupling between overwind and linear has been considered based on two extreme idealizations. In the first, the overwind is rigidly coupled with the liner, so that the two deform together in the meridional direction as the vessel dilates. In the second, the overwind is free to slide relative to the linear, but the overall elongations of the two around a meridian are identical. Optimized designs with the two idealizations show only minor differences, and it is concluded that either approximation is satisfactory for the purposes of vessel design. Aspects taken into account are the intrinsic overwind thickness variation arising from the winding process and the effects of fiber pre-tension. Pre-tension can be used not only to defer the onset of yielding, but also to achieve a favorable in-plane stress ratio which minimizes the von Mises equivalent stress in the metal liner. Aramid fibers are the most appropriate fibers to be used for the overwind in this type of application. The quantity of fiber required is determined by both its short-term strength and its long-term stress rupture characteristics. An optimization procedure for the design of such vessels, taking all these factors into account, has been established. The stress distributions in the vessels designed in this way have been examined and discussed through the examples. A design which gives due consideration of possible mechanical damage to the surface of the overwind has also been addressed.

Characterization of Flow Stress for Commercially Pure Titanium Subjected to Electrically-Assisted Deformation

2013 ◽  
Author(s):  
James Magargee ◽  
Fabrice Morestin ◽  
Jian Cao
Keyword(s):  
Flow Stress ◽  
Heating Temperature ◽  
Pure Titanium ◽  
Constitutive Models ◽  
Plastic Behavior ◽  
Commercially Pure Titanium ◽  
Coupled Models ◽  
Commercially Pure ◽  
Electrically Assisted ◽  
Tension And Compression

Uniaxial tension tests were conducted on thin commercially pure titanium sheets subjected to electrically-assisted deformation using a new experimental setup to decouple thermal-mechanical and possible electroplastic behavior. The observed absence of stress reductions for specimens air-cooled to near room temperature motivated the need to reevaluate the role of temperature on modeling the plastic behavior of metals subjected to electrically-assisted deformation, an item that is often overlooked when invoking electroplasticity theory. As a result, two empirical constitutive models, a modified-Hollomon and the Johnson-Cook models of plastic flow stress, were used to predict the magnitude of stress reductions caused by the application of constant DC current and the associated Joule heating temperature increase during electrically-assisted tension experiments. Results show that the thermal-mechanical coupled models can effectively predict the mechanical behavior of commercially pure titanium in electrically-assisted tension and compression experiments.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

2016 ◽  
Vol 08 (04) ◽  
pp. 1650054 ◽  
Author(s):  
Zeinab Mazarei ◽  
Mohammad Zamani Nejad ◽  
Amin Hadi
Keyword(s):  
Heat Flux ◽  
Functionally Graded Materials ◽  
Poisson’S Ratio ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Material Behavior ◽  
Poisson's Ratio ◽  
Uniform Heat Flux ◽  
Plastic Behavior ◽  
Graded Materials

An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, the effect of increasing the heat flux and pressure on the propagation of the plastic zone are investigated. Furthermore, the effect of change in Poisson’s ratio on the value of the critical material parameter is demonstrated. The present study is also validated by comparing the numerical results for thick elasto-plastic spherical shells available in the literature. To the best of the authors’ knowledge, in previous studies, exact thermo-elasto-plastic behavior of FGM thick-walled sphrical pressure vessels has not investigated.

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