Comparison of semi and fully-implicit time integration schemes applied to a damage and fatigue phase field model

Haveroth, Geovane A.; Moraes, Eduardo A. Barros de; Boldrini, José Luiz; Bittencourt, Marco L.

doi:10.1590/1679-78254383

Cited by 9 publications

(6 citation statements)

References 18 publications

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“…We adopt a semiimplicit time integration scheme, where we solve each equation separately using a suitable implicit method, treating nonlinear terms and other variable fields explicitly. The methodology is based on the work by Haveroth et al, 20 where a detailed derivation can be found. We split the solution time interval [0, T ] in discrete time steps t n with time increments given by

Δ t = t_{n + 1} - t_{n} > 0

, n = 0, 1, ….…”

Section: A Stochastic Damage and Fatigue Phase‐field Frameworkmentioning

confidence: 99%

“…17 Boldrini et al 18 developed a nonisothermal and thermodynamically consistent framework for damage and fatigue using phase-fields. Spatial convergence and two-dimensional (2D) results were presented by Chiarelli et al 19 A comparison between semi and fully implicit time integration schemes was analyzed by Haveroth et al 20 Despite the ability to describe crack geometry and incorporate naturally fatiguing mechanisms and different constitutive laws, most examples of phase-field solutions studied so far include geometric characteristics that drive the crack path to determined places. The presence of notches, indentations, regions of stress concentration, is recurrent and leads to controlled experiments with a predictable crack path (always assuming a perfect material).…”

Section: Introductionmentioning

confidence: 99%

“…Boldrini et al 18 developed a nonisothermal and thermodynamically consistent framework for damage and fatigue using phase‐fields. Spatial convergence and two‐dimensional (2D) results were presented by Chiarelli et al 19 A comparison between semi and fully implicit time integration schemes was analyzed by Haveroth et al 20 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An integrated sensitivity‐uncertainty quantification framework for stochastic phase‐field modeling of material damage

Moraes

Zayernouri

Meerschaert

2020

Int J Numer Methods Eng

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Materials accumulate energy around voids and defects under external loading, causing the formation of microcracks. With increasing or repeated loads, those microcracks eventually coalesce to form macrocracks, which in a brittle material can cause catastrophic failure without apparent permanent deformation. At the continuum level, a stochastic phase-field model is employed to simulate failure through introducing damage and fatigue variables. The damage phase-field is introduced as a continuous dynamical variable representing the volumetric portion of fractured material and fatigue is treated as a continuous internal field variable to model the effects of microcracks arising from energy accumulation. We formulate a computational-mathematical framework for quantifying the corresponding model uncertainties and sensitivities in order to unfold and mitigate the salient sources of unpredictability in the model, hence, leading to new possible modeling paradigms. Considering an isothermal isotropic linear elastic material with viscous dissipation under the hypothesis of small deformations, we employed Monte Carlo and probabilistic collocation methods to perform the forward uncertainty propagation, in addition to local-to-global sensitivity analysis. We demonstrate that the model parameters associated with free-energy potentials contribute significantly more to the total model output uncertainties, motivating further investigations for obtaining more predictable model forms, representing the damage diffusion.

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Δ t = t_{n + 1} - t_{n} > 0

, n = 0, 1, ….…”

Section: A Stochastic Damage and Fatigue Phase‐field Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An integrated sensitivity‐uncertainty quantification framework for stochastic phase‐field modeling of material damage

Moraes

Zayernouri

Meerschaert

2020

Int J Numer Methods Eng

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“…The inclusion of fatigue effects was initially attempted with Ginsburg-Landau free-energy potentials (Amendola et al, 2016) and fractional derivatives (Caputo and Fabrizio, 2015). A more general framework for damage and fatigue was later developed in a nonisothermal and thermodynamically consistent approach (Boldrini et al, 2016;Chiarelli et al, 2017;Haveroth et al, 2018), followed by the emergence of further phase-field models for fatigue (Carrara et al, 2019;Seiler et al, 2019). Within this myriad of different models, solution uncertainty and parametric sensitivity are still influential, and the predictability of phase-field models for arbitrary conditions is yet a withstanding effort (Barros de Moraes et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Failure Prediction in Brittle Materials: A Phase Field-Based Machine Learning Framework

Moraes

Salehi

Zayernouri

2021

J Mach Learn Model Comput

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Failure in brittle materials led by the evolution of micro-to macro-cracks under repetitive or increasing loads is often catastrophic with no significant plasticity to advert the onset of fracture. Early failure detection with respective location are utterly important features in any practical application, both of which can be effectively addressed using artificial intelligence. In this paper, we develop a supervised machine learning (ML) framework to predict failure in an isothermal, linear elastic and isotropic phase-field model for damage and fatigue of brittle materials. Time-series data of the phase-field model is extracted from virtual sensing nodes at different locations of the geometry. A pattern recognition scheme is introduced to represent time-series data/sensor node responses as a pattern with a corresponding label, integrated with ML algorithms, used for damage classification with identified patterns. We perform an uncertainty analysis by superposing random noise to the time-series data to assess the robustness of the framework with noise-polluted data. Results indicate that the proposed framework is capable of predicting failure with acceptable accuracy even in the presence of high noise levels. The findings demonstrate satisfactory performance of the supervised ML framework and the applicability of artificial intelligence and ML to a practical engineering problem, i.e., data-driven failure prediction in brittle materials.

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“…Mesh locking due to geometric properties and material incompressibility are bypassed with the HOFEM only by increasing the polynomial order above four of the mesh elements as presented in [2,35,36]. The use of the HOFEM for the analysis of a phase field model for fracture, damage and fatigue is discussed in [37,38,39] and Mortar contact finite elements are presented in [40,41]. There have also been applications on capturing the instability waves arising in near-wall flow interactions [42].…”

Section: Introductionmentioning

confidence: 99%

Simulation of non-linear structural elastodynamic and impact problems using minimum energy and simultaneous diagonalization high-order bases

Dias,

Suzuki,

Valente

et al. 2021

Preprint

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We present the application of simultaneous diagonalization and minimum energy (SDME) high-order finite element modal bases for simulation of transient non-linear elastodynamic problem, including impact cases with neohookean hyperelastic materials. The bases are constructed using procedures for simultaneous diagonalization of the internal modes and Schur complement of the boundary modes from the standard nodal and modal bases, constructed using Lagrange and Jacobi polynomials, respectively. The implementation of these bases in a high-order finite element code is straightforward, since the procedure is applied only to the one-dimensional expansion bases. Non-linear transient structural problems with large deformation, hyperelastic materials and impact are solved using the obtained bases with explicit and implicit time integration procedures. Iterative solutions based on preconditioned conjugate gradient methods are considered. The performance of the proposed bases in terms of the number of iterations of pre-conditioned conjugate gradient methods and computational time are compared with the standard nodal and modal bases. Our numerical tests obtained speedups up to 41 using the considered bases when compared to the standard ones.

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Comparison of semi and fully-implicit time integration schemes applied to a damage and fatigue phase field model

Cited by 9 publications

References 18 publications

An integrated sensitivity‐uncertainty quantification framework for stochastic phase‐field modeling of material damage

An integrated sensitivity‐uncertainty quantification framework for stochastic phase‐field modeling of material damage

Data-Driven Failure Prediction in Brittle Materials: A Phase Field-Based Machine Learning Framework

Simulation of non-linear structural elastodynamic and impact problems using minimum energy and simultaneous diagonalization high-order bases

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