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Numerical calibration of material parameters of selected directional distortional hardening models with combined approach using both distorted yield surfaces and stress-strain curves
Hrubý, Zbyněk ; Plešek, Jiří ; Parma, Slavomír ; Marek, René ; Feigenbaum, H. P. ; Dafalias, Y.F.
The plastic strain induced anisotropy is a well-known phenomenon in manufacturing and directional distortional hardening represents a very promising way to capture real plastic behavior of metals. Many papers were published in the past typically extending the von Mises yield criterion with directionally dependent internal variable and defining yield point at the basis of plastic strain offset. Material parameters of these models were typically calibrated at the basis of deformed yield surfaces only, which – as revealed – could lead to certain discrepancies in simple stress-strain response. Presented paper introduces a numerical calibration approach taking both distorted yield surfaces and stress-strain curves information into account. Besides the calibration procedures, innovative applications of experimental techniques such as the acoustic emission for an acquisition of yield inception and plastic straining, convexity of the models, or numerical implementation of these models are discussed.
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Využití numerické zpětné laplaceovy transformace při řešení úloh elastodynamiky
Adámek, V. ; Valeš, František ; Červ, Jan
Laplaceova transformace představuje jednu z nejvíce užívaných transformací v časové oblasti. Existují dva přístupy při hledání inversní Laplaceovy transformace, analytický a numerický. Analytická metoda je založena na exaktním vyjádření inversního integrálu pomocí Cauchyovy residuové věty. Podstata druhé metody spočívá v numerickém řešení inversního integrálu. Ukazuje se, že numerický přístup je rychlejší nežli analytické řešení. V neposlední řadě může být tento přístup využit ve složitějších případech, kde např. existence bodů rozvětvení činí inversní proces, založený na analytickém přístupu, mnohem komplikovanější.
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New method of complex modulus estimation of prepressed rubber by the FE model parameter tuning – rubber-damped wheel application
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Cibulka, Jan ; Boháč, T. ; Tašek, H.
The main goal of the study was to develop a method for estimation of the frequency dependence of material constants of the pre-pressed hard synthetic rubbers. It was motivated the need to identify material constants, i.e. Young modulus and loss factor, of rubber segments pressed between the disk and the rim of a rubber-damped railway wheel. The rubber segments are pre-pressed about 20% strain level during the production of the wheel. Hard synthetic rubber materials exhibit complex thermalfrequency behavior with nonlinear dependence on static preload. The standard experimental procedures that evaluate the frequency dependence of the material are based on the vibrations of a cantilever beam that consists of a metal and a rubber layer. The new estimation method of the complex modulus of elasticity of rubber is based on the tuning of rubber constants of an FE wheel model according to the results of natural frequencies and mode shapes of the wheel ascertained from the experiment. Numerical FE model of the wheel consisted of the cyclic model of 1/24 sector of the wheel with an angle of 15° and containing one rubber segment and was created in ANSYS 14.5. Damping model of rubber is described by a special case of proportional damping. For calculating eigenvalues of the problem, the Lanczos method was used for the wheel as an undamped system and QR damped method for the damped system. The experimental modal analysis of the rubber-damped wheel pressed on the shaft took place at room temperature in the dynamic laboratory. Modal tests were performed in configuration with an exciter acting first in the axial direction and consequently in the radial direction of the wheel. Responses to the exactions were measured in three directions at 144 points. The identification of eigenvalues and mode shapes of the wheels was made separately for excitations both in radial and in axial direction.
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