Analytical and finite element solutions of some problems using a viscoplastic model

The feasibility of advanced viscoplastic models for non-linear boundary element analysis of metallic structural components with dependence on thermomechanical history is investigated.Several numerical examples are presented using the boundary element implementation of two different internal state variable viscoplastic models to the solution of time-dependent inelastic problems arising in creeping metallic structural components under the combined action of high temperature loading gradients and quasi-static mechanical loading conditions. To demonstrate the efficiency of the implemented viscoplastic models, the results obtained using the direct boundary element methodology are compared with those obtained by both analytical and finite element solution as well as, for different numerical results of plane strain thermoviscoplastic deformation problems under general thermomechanical loading. IntroductionRecently a number of stress-strain constitutive models known as viscoplastic models have emerged. This is due to the effort to improve the high-temperature performance of structural components used in aerospace and nuclear industry. Inelasticity does not occur in these components as a result of mechanical loading but is induced mainly through thermal transient cycles and thermal gradients. The conventional constitutive equations and damage models fail to reflect the strong thermomechanical path dependence observed in, for example, the cyclic hardening behavior of some metals and alloys especially in the presence of metallurgical changes. So that the development of some realistic viscoplastic models accompanied by appropriate constitutive equations was crucial for the design of high-temperature energy system components. The motivation of these viscoplastic models was the treatment of all the inelastic strains (plastic, creep, relaxation, etc.) as a single quantity and this automatically includes any interaction among them. These viscoplastic models are intended to provide reliable derivation of this high-temperature,

show abstract

“…Those formulas have been derived earlier by Mukherjee (1979), Cordts and Kollman (1986) and Arya (1989).…”

Section: Analytical Solutionsmentioning

confidence: 91%

Viscoplastic D/BEM analysis of metallic structures with dependence on thermomechanical history

Providakis

Kourtakis

2002

Engineering Computations

View full text Add to dashboard Cite

show abstract

“…Кроме того, многими специалистами задачи по исследованию толстостенных сфер решались с помощью других моделей: аналитических, численных и конечно-элементных. При этом использовались решения моделей композиционных материалов, охватывающие различные стадии работы материала: упруго-пластическую [5], вязко-пластическую [6], ползучести [7; 8]. Рассматри- вались также задачи с применением материалов с различными прочностными и упруго-пластическими свойствами, в том числе упругопластических [5; 9-11], вязкопластических [6], функционально-градиентных [12] и подверженные воздействию силовых и не силовых нагрузок: осесимметричных [13], объемных сил [13], внешнего и внутреннего давления [10], гидростатического давления [14], коррозионно-активных сред [5], циклически действующих температур [9], электромагнитных и термомеханических нагрузок [15].…”

Section: Introductionunclassified

Multitudes of Voigt - Reuss forks and Voigt - Christensen - Reuss tridents

Erofeev

Трофимович²,

Tyuryakhin

et al. 2020

Struct. Mech. of Eng. Const. and Build

View full text Add to dashboard Cite

In the literature, there are many studies of the representative volume of a composite material, in particular, those calculated using the formulas of Christensen, Voigt and Reiss. The aim of this work is to study the features of evaluating the set of forks of effective modules. Methods. On the basis of solving the Lame problem (for a thick-walled sphere), a spherical model of a representative volume (cell) of a composite material with a granular (spherical) filler is compiled and the value of the effective modulus of elasticity of a two-phase composite is determined. The study of the obtained formula for the effective modulus, expressed in dimensionless quantities, for the cell material revealed its identity with the R.M. Christensens formula, expressed in dimensional values, for the bulk modulus of composites with a spherical filler. In this case, Christensens solution was previously obtained by a different method when he considered the polydisperse model of the composite. The dimensionless form of the function (effective module) of three dimensionless parameters made it possible in flat spaces (two coordinate planes) to construct graphical images of the function of the named modules according to Christensen, which are compared and combined in one figure with similar images of the functions of estimating the values of the modules (real composites) according to Voigt and Reiss. Graphical studies in relation to the spherical representative volume model show that in the flat space of the set of Voigt - Reuss forks, these forks are not narrowed, but they are partially filled by the flat space of the set of Christensen - Reiss forks. The graphs of the functions of the modules, at the same time, form, simultaneously with the sets of two-toothed forks, a set of Voigt - Christensen - Reiss trident forks (tridents), which, depending on the size of the intervals of the numbers of the studied parameters, have forks of different sizes. Results. Graphic illustrations of numerical examples have been obtained showing that for given values of the module of the matrix and filler and the volume fraction of the latter, it is possible to determine the effective volumetric module and shear module of two-phase composites, and to perform a comparison with the conclusions of the applied plan. The dimensionless form of the obtained expressions makes it possible to solve the inverse problems of the mechanics of polydisperse composites, for example, to determine the volume module of the composite components by the effective modulus obtained by mechanical testing of standard samples.

show abstract

“…Furthermore, the 3-D Navier equations of elasticity and the Kirchhoff constraints were used for the development of the finite element model. In 1989, Arya presented an analytical and finite element solution for some problems by using a viscoplastic model [21]. This researcher performed a nonlinear structural analysis.…”

Section: Introductionmentioning

confidence: 99%

Stress Analysis by Two Cuboid Isoparametric Elements

Rezaiee‐Pajand

Karimipour

2019

TECM

View full text Add to dashboard Cite

The finite element method is a powerful tool for solving most of the structural problems. This technique has been used extensively, since the complexity of the elastic field equations does not allow the specialist to find analytical solutions, especially for the three-dimensional structures. It is well-known that the finite element formulation yields the approximate stress responses. To remedy this defect, the Airy stress function is utilized in this study. The stress function formulation leads to a valid solution since it satisfies equilibrium and compatibility equations simultaneously. Two cuboid isoparametric elements are formulated for solving three-dimensional elastic structures. To demonstrate the performance of the proposed technique, various benchmark problems are analyzed. The errors between the exact, displacement-based finite element and recommended scheme solution are also calculated. All the obtained outcomes show the good merit of the presented new elements.

show abstract

Analytical and finite element solutions of some problems using a viscoplastic model

Cited by 17 publications

References 4 publications

Viscoplastic D/BEM analysis of metallic structures with dependence on thermomechanical history

Viscoplastic D/BEM analysis of metallic structures with dependence on thermomechanical history

Multitudes of Voigt - Reuss forks and Voigt - Christensen - Reuss tridents

Stress Analysis by Two Cuboid Isoparametric Elements

Contact Info

Product

Resources

About