New formulation of nonlinear kinematic hardening model, Part I: A Dirac delta function approach

Okorokov, Volodymyr; Gorash, Yevgen; Mackenzie, Donald; Rijswick, Ralph van

doi:10.1016/j.ijplas.2019.07.006

Cited by 16 publications

(2 citation statements)

References 57 publications

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“…In the previous work [4, 9], the hardening ratio

\rho _{h}

is assumed to be constant (

k_{h}=1

) during the whole cyclic loading process. However, some researchers [5, 10, 11] indicated that the hardening rate changes significantly after shear reverse loading condition. Compared to the multi‐surfaces [10] and multi‐kinematic‐hardening‐parameters approach [11], the most straightforward effective hardening function

$$\begin{equation} k_{h}={\left\lbrace \def\eqcellsep{&}\begin{array}{llccccc} 0 &\,\mbox{for}\, & \gamma ^{*} \le 0.05&\mbox{and}\, & \gamma ^{*}&lt;\gamma \\[3pt] 1-e^{-60(\gamma ^{*}-0.05)}{+(10\gamma ^{*}-0.5)e^{-6}}&\,\mbox{for}\, & 0.05&lt;\gamma ^{*} \le 0.15&\mbox{and}\, & \gamma ^{*}&lt;\gamma \\[3pt] 1 &\,\mbox{for}\, & 0.15&lt;\gamma ^{*} &lt;\gamma &\mbox{or} \, &\gamma ^{*}\ge \gamma \end{array} \right.}\,.

…”

Section: Constitutive Modelingmentioning

confidence: 99%

“…In the previous work [4,9], the hardening ratio 𝜌 ℎ is assumed to be constant (𝑘 ℎ = 1) during the whole cyclic loading process. However, some researchers [5,10,11] indicated that the hardening rate changes significantly after shear reverse loading condition. Compared to the multi-surfaces [10] and multi-kinematic-hardeningparameters approach [11], the most straightforward effective hardening function…”

Section: Constitutive Modelingmentioning

confidence: 99%

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Characterization of ductile damage and fracture behavior under shear reverse loading conditions

Wei,

Gerke,

Brünig

2023

Proc Appl Math and Mech

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This paper deals with experimental and numerical analysis of the ductile damage and fracture behavior undergoing biaxial non‐proportional shear reverse loading conditions. In the numerical analysis, an anisotropic cyclic plastic‐damage constitutive model is considered to characterize the damage and fracture behavior. Additionally, the change in the hardening rate is observed after shear reverse loading. Thus, a newly modified non‐hardening strain region method is introduced to capture the change in the hardening ratio between isotropic and kinematic hardening. Furthermore, the damage surface is assumed to translate in the direction of the damage strain increment. Hence, a softening law based on the damage strain is proposed. The modified constitutive model predicts macroscopic force‐displacement and microscopic evolution of plastic and damage behaviors under shear reverse loading with a tensile preload. Through digital image correlation technique and scanning electron microscopy, numerical results can be validated by experimental ones. Furthermore, scanning electron microscopy pictures also reveal different damage and fracture mechanisms on the micro‐level.

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“…In the previous work [4, 9], the hardening ratio

\rho _{h}

is assumed to be constant (

k_{h}=1

$$\begin{equation} k_{h}={\left\lbrace \def\eqcellsep{&}\begin{array}{llccccc} 0 &\,\mbox{for}\, & \gamma ^{*} \le 0.05&\mbox{and}\, & \gamma ^{*}&lt;\gamma \\[3pt] 1-e^{-60(\gamma ^{*}-0.05)}{+(10\gamma ^{*}-0.5)e^{-6}}&\,\mbox{for}\, & 0.05&lt;\gamma ^{*} \le 0.15&\mbox{and}\, & \gamma ^{*}&lt;\gamma \\[3pt] 1 &\,\mbox{for}\, & 0.15&lt;\gamma ^{*} &lt;\gamma &\mbox{or} \, &\gamma ^{*}\ge \gamma \end{array} \right.}\,.

…”

Section: Constitutive Modelingmentioning

confidence: 99%

Section: Constitutive Modelingmentioning

confidence: 99%

Characterization of ductile damage and fracture behavior under shear reverse loading conditions

Wei,

Gerke,

Brünig

2023

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

Full probabilistic analysis of random first‐order linear differential equations with Dirac delta impulses appearing in control

López

Delgadillo-Aleman

Kú-Carrillo

et al. 2021

Math Methods in App Sciences

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We study, from a probabilistic standpoint, first‐order impulsive linear differential equations, where all its parameters (initial condition and coefficients) are absolutely continuous random variables with a joint probability density function. We assume an infinite train of Dirac delta impulse applications at given time instants to control the model output. We take extensive advantage of the random variable transformation method to determine, first, an explicit expression for the probability density of the solution stochastic process, and secondly, of the random sequences for the maxima and minima. From these sequences, we determine the probability of stability of the solution stochastic process. This analysis is extended in the case that the application times are evenly spaced, via a period T, which is assumed to be a random variable. All the theoretical results are illustrated by means of several numerical examples, where we also perform a sensitivity analysis, via Sobol indexes, to highlight those model parameters that most explain the variability of the model response.

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Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

Shutov,

Kaygorodtseva,

Zakharchenko

et al. 2024

Z Angew Math Mech

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This paper provides new experimental data regarding inelastic strain accumulation in structural steel samples. The samples are subjected to stress‐controlled cyclic loading with positive mean stress within each cycle; the loading blocks are combined in a complex pattern to study the effect of load history. A large‐strain ratcheting model is constructed based on a material law with a nonlinear kinematic and isotropic hardening. A new rule of ductile damage accumulation is suggested and a class of models with hardening stagnation is introduced. We show that models which include the hardening stagnation describe the experimental data more accurately. Unfortunately, due to a large spread of mechanical properties from sample to sample, it is impossible to describe the entire set of experiments using a single set of parameters. To address this challenge, we have developed novel mathematical tools for parameter identification in the context of stochastic variations in mechanical properties. These tools include the concept of a collar of model responses and the notion of protrusion. We propose an extended parameter identification problem that rethinks the standard error functional. We demonstrate that the extended identification problem effectively accounts for the large spread observed in experimental data when applied to the developed ratcheting model.

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New formulation of nonlinear kinematic hardening model, Part I: A Dirac delta function approach

Cited by 16 publications

References 57 publications

Characterization of ductile damage and fracture behavior under shear reverse loading conditions

Characterization of ductile damage and fracture behavior under shear reverse loading conditions

Full probabilistic analysis of random first‐order linear differential equations with Dirac delta impulses appearing in control

Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

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