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1

A comparative study of various models of equivalent plastic strain to fracture

Mykhalevych Volodymyr, Dobraniuk Yurii, Matviichuk Victor, Kraievskyi Volodymyr, Тiutiunnyk Oksana, Smailova Saule, Kozbakova Ainur

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2023

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T. 13, nr 1

64--70

EN

For more then half a centre just the same approach to the simulation of the ductile crack formation wasdeveloped independently by the scientific communities of foreign and native researchers. The importance at these studies drastically increased. A set of the characteristics, according to whichit is recommendly to perform thedetail comparison of the existing fracture models is developed. The examples of the analysis of a number of the most popular models by means of obtaining and study their analytical expressions regarding the conditions of the plane state are given. The generalized relations of the know models and a number of separate relations are obtained.

PL

Od ponad pół wieku to samo podejście do modelowania uszkodzeń podczas odkształceńplastycznych jest opracowywane niezależnie przez zespoły naukowe złożone znaukowców zagranicznych i krajowych. W ostatnich dziesięcioleciach znaczenie tych badań dramatycznie wzrosło. Opracowano zestaw cech, zgodnie z którymi proponuje się przeprowadzenie szczegółowego porównania istniejących modeli zniszczenia. Podano przykłady analizy szeregu najpopularniejszych modeli poprzez uzyskanie i badanie ich wyrażeń analitycznych dla warunków płaskiego stanunaprężenia. Otrzymano uogólnione wskaźniki znanych modeli oraz szereg wskaźników indywidualnych.

2

Instabilities in membrane tension: Parametric study for large strain thermoplasticity

Mucha M., Wcisło B., Pamin J., Kowalczyk-Gajewska K.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 4

1055--1067

EN

This paper deals with the numerical analysis of localized deformation for a rectangular plate in membrane tension, modelled with large strain thermoplasticity. The aim is to determine the influence of selected factors on the localization phenomena, which can result from geometrical, material, and thermal softening. Two types of boundary conditions are considered: plane stress and plane strain, as well as two yield functions, Huber–Mises–Hencky and Burzyński–Drucker–Prager, with selected values of friction angle. First, isothermal conditions are considered and next, a conductive case with thermal softening is studied. Moreover, three types of plastic behaviour are analysed: strain hardening (with different values of hardening modulus), ideal plasticity, and strain softening. Numerical tests, performed using AceGen/FEM packages, are carried out for the rectangular plate under tension with an imperfection, using three finite element discretizations. The results for plane strain in the isothermal model show that with the decrease of linear hardening modulus, we can observe stronger mesh sensitivity, while for plane stress, mesh sensitivity is visible for all cases. Furthermore, for the thermomechanical model the results also depend on the mesh density due to insufficient heat conduction regularization.

3

Analytical solution of mixed boundary value problems using the displacement potential approach for the case of plane stress and plane strain conditions

Deb Nath S. K.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 2

269--291

EN

Two elastic plate problems made of duralumin are solved analytically using the displacement potential approach for the case of plane strain and plane stress conditions. Firstly, a one end fixed plate is considered in which the rest of the edges are stiffened and a uniform load is applied to the opposite end of the fixed end. Secondly, a plate is considered in which all of the edges are stiffened and a uniform tension is applied at its both ends. Solutions to both of the problems are presented for the case of plane stress and plane strain conditions. The effects of plane stress and plane strain conditions on the solutions are explained. In the case of stiffening of the edges of the plate, the shape of the plate does not change abruptly, which is clearly observed in both of the cases. For the plane strain condition, the plates become stiffer in the loading direction as compared to the plane stress condition. For the plane strain condition, there is a significant variation of the normal stress component, σzz at different sections of the plate. The graphical results, clearly identify the critical regions of the plate for the case of the plane stress and plane strain condition.

4

Computational modeling of creep in complex plane for reinforced materials

Monfared V.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 6

909--916

EN

Computational modeling for predicting the steady state creep behavior is presented in complex plane for reinforced materials by complex variable method. Both the fiber and matrix simultaneously creep at elevated temperatures and loading. We suppose that one dimension of the short fiber is small enough in comparison with the other two (see Fig. 1). In this formulation, plane stress state is used. Finally, displacement rate behaviors are predicted using compatibility, equilibrium, constitutive, and governing equations by complex variable method. One of the considerable applications of the method is in nano-composites analysis in elasticity or plasticity research.

5

Damage initiation mechanism in rubber sheet composites during the static loading

Luong R., Isac N., Bayraktar E.

Archives of Materials Science and Engineering

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2007

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Vol. 28, nr 1

19-26

EN

Purpose: Mechanical behaviour and damage initiation mechanisms in thin rubber sheet composites were investigated under static solicitation at room temperature. Two types of rubber are used in this study; Natural rubber, NR vulcanised and reinforced by carbon black and Synthetic rubber (styrene-butadiene-rubber, SBR). Design/methodology/approach: A comprehensive study has been carried out in order to identify a threshold criterion for the damage mechanism to explain a tearing criterion for the concept of tearing energy of the elastomers and also to give a detail for the damage mechanism depending on the loading conditions. A typical type of specimen geometry of thin sheet rubber composite materials was studied under static tensile tests conducted on the smooth and notched specimens with variable depths. In this way, the effects of the plane stress on the damage mechanism are characterized depending on the rubber materials. Findings: Damage mechanisms during tensile test have been described for both of rubber types and the criteria which characterize the tearing resistance, characteristic energy for tearing (T) was explained. Damage in the specimens were evaluated just at the beginning of the tearing by means of the observations in the scanning electron microscopy (SEM). Practical implications: A tearing criterion was suggested in the case of simple tension conditions by assuming large strain. In the next step of this study, a finite element analysis (FEA) will be applied under the same conditions of this part in order to obtain the agreement between experimental and FEA results. Originality/value: This study propses a threshold criterion for the damage just at the beginning of the tearing for thin sheet rubber composites and gives a detail discussion for explaining the damage mechanisms by SEM results. This type of study gives many facilities for the sake of simplicity in industrial application.

6

Hybrid NN/FEM analysis of the elastoplastic plane stress problem

Waszczyszyn Z., Pabisek E.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 2

177-188

EN

The back-propagation neural network was trained off line in order to simulate operation of the return mapping algorithm. Selection of patterns and the neural network training as well as testing processes are discussed in detail. The network was incorporated into the FE computer code ANKA as a neural procedure. The hybrid neural-network/finite-element-method program ANKA-H was used for the analysis of two elastoplastic plane stress examples: i) perforated tension strip, ii) notched beam. The results of computations point out quite good accuracy of the hybrid analysis. Some prospects of development of hybrid NN/FEM programs are given at the end of paper.