Accelerated time integrator for multiple time scale homogenization

Crouch, Robert D.; Oskay, Caglar

doi:10.1002/nme.4863

Cited by 20 publications

(13 citation statements)

References 35 publications

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“…The capability of the method was demonstrated for a ceramic composite [70] simulating its material response by a continuum damage model. In line with the assumption of the scale separation, the equilibrium state over the fine temporal scale was taken to be unaffected by the change in the damage state [71]. The respective equilibrium problem becomes linear and can be efficiently solved with the conventional methods of the linear algebra.…”

Section: Review Of Approachesmentioning

confidence: 99%

Computational Methods for Lifetime Prediction of Metallic Components under High-Temperature Fatigue

Kindrachuk

Fedelich

Rehmer

et al. 2019

Metals

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The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.

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Section: Review Of Approachesmentioning

confidence: 99%

Computational Methods for Lifetime Prediction of Metallic Components under High-Temperature Fatigue

Kindrachuk

Fedelich

Rehmer

et al. 2019

Metals

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“…The power law multiplier

{false({\overset{ε}{true}}^{eq} false/ normalκ false)}^{n} \leq 1

with a material coefficient n >0 governs the damage rate below the “failure surface” . Similar fatigue laws have been adopted in other works,() where the damage equivalent strain and energy release rate were considered as the driving force for damage.…”

Section: Overview Of the Governing Equationsmentioning

confidence: 99%

“…In this paper, the function

normalΦ false({\overset{ε}{true}}^{eq} false)

is defined as

normalΦ false({\overset{ε}{true}}^{eq} false) = \frac{\arctan \frac{{\overset{ε}{true}}^{eq} - e_{0}}{e_{f}} + \arctan \frac{e_{0}}{e_{f}}}{2 \arctan 1 + \arctan \frac{e_{0}}{e_{f}}},

based on the works of Fish and Yu() and Crouch and Oskay. () Note that the initial value of κ in is zero κ(0)=Φ −1 (0)=0. In this simplified consideration, fatigue is assumed to proceed at any level of loading provided that

{\overset{\overset{ε}{true}}{true}}^{eq} > 0

.…”

Section: Overview Of the Governing Equationsmentioning

confidence: 99%

“…The displacement field can then be reconstructed by taking the solutions of , ie,

bold-italicu \approx true \sum_{k = - k^{*}}^{k^{*}} u_{k} false(Υ false) e^{i k normalω normalτ} .

Similarly, quasi‐linear approximations of the microchronological problem have been successfully realized in the works of Kindrachuk and Unger() and Crouch and Oskay. () Adopting such a mathematical treatment is however ineffective to get the microchronological solution for the nonlocal equivalent strain . Indeed, the discretized averaging equation is nonlinear with respect to u (see, for instance, equation ).…”

Section: Ftti Schemementioning

confidence: 99%

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A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue

Kindrachuk

Titscher

Unger

2018

Numerical Meth Engineering

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Summary A key limitation of the most constitutive models that reproduce a degradation of quasi‐brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations. The essential constituent of the fatigue model is an implicit gradient‐enhanced formulation of the damage rate. The evolution of the field variables is computed as a multiscale Fourier series in time. On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarser macrochronological scale associated with the duration of material deterioration. The performance of the developed method is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.

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“…In order to address the presence of multiple time scales, the long term performance of structures subjected to cyclic loading are traditionally modeled using cycle-jump approaches (see e.g., [11]). More recently, an alternative methodology based on the multiple time scale computational homogenization has been developed by Oskay and Fish [29,30] to investigate the failure behavior of a range of materials from metals [30,16] to composites [13,14,3].…”

Section: Introductionmentioning

confidence: 99%

Multi-Yield Surface Modeling of Viscoplastic Materials

Yan

Oskay

2017

Int J Mult Comp Eng

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This manuscript presents a multi-yield surface model to idealize the mechanical behavior of viscoplastic solids subjected to cyclic loading. The multi-yield surface model incorporates the evolution of nonlinear viscoplastic flow through a piece-wise linear hardening approximation. A kinematic hardening law is employed to account for the evolution of backstress with respect to the viscoplastic strain rate. The new backstress evolution strategy is proposed to ensure that all yield surfaces remain consistent (i.e., satisfying collinearity) throughout the viscoplastic process. The multi-yield surface model is coupled with viscoelasticity to approximate the relaxation behavior of high temperature metal alloys. The model is implemented using a mixed finite element approach. The capabilities of the proposed approach are demonstrated using experiments conducted on a high temperature titanium alloy (Ti-6242S) subjected to static, cyclic and relaxation conditions.

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Accelerated time integrator for multiple time scale homogenization

Cited by 20 publications

References 35 publications

Computational Methods for Lifetime Prediction of Metallic Components under High-Temperature Fatigue

Computational Methods for Lifetime Prediction of Metallic Components under High-Temperature Fatigue

A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue

Multi-Yield Surface Modeling of Viscoplastic Materials

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