Physics-informed machine learning model for computational fracture of quasi-brittle materials without labelled data

Zheng, Bin; Li, Tongchun; Qi, Huijun; Gao, Lingang; Liu, Xiaoqing; Yuan, Li

doi:10.1016/j.ijmecsci.2022.107282

Cited by 49 publications

(16 citation statements)

References 34 publications

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“…The training process was manually terminated after identifying an interpretable and highly accurate individual. The operators ' + ' , ' -' , ' × ' , ' / ' , 'ln_abs() ' (24)…”

Section: Domain Knowledge-guidedmentioning

confidence: 99%

“…Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities. It has been widely used for crack growth to solve complex nonlinear prediction problems [18][19][20][21][22][23][24][25]. Indeed, the radial basis function artificial neural network (RBF-ANN), backpropagation neural network (BPNN), extreme learning machine (ELM), fully connected neural network, random forest (RF), hidden Markov model (HMM), and long short-term memory (LSTM) all yield accurate life and crack growth predictions [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Zhou

Yang

Xiao

et al. 2023

Chin. J. Mech. Eng.

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Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities, so it has been widely utilised in the fatigue field. However, most ML methods are inexplicable black-box models that are difficult to apply in engineering practice. Symbolic regression (SR) is an interpretable machine learning method for determining the optimal fitting equation for datasets. In this study, domain knowledge-guided SR was used to determine a new fatigue crack growth (FCG) rate model. Three terms of the variable subtree of ΔK, R-ratio, and ΔKth were obtained by analysing eight traditional semi-empirical FCG rate models. Based on the FCG rate test data from other literature, the SR model was constructed using Al-7055-T7511. It was subsequently extended to other alloys (Ti-10V-2Fe-3Al, Ti-6Al-4V, Cr-Mo-V, LC9cs, Al-6013-T651, and Al-2324-T3) using multiple linear regression. Compared with the three semi-empirical FCG rate models, the SR model yielded higher prediction accuracy. This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

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“…The training process was manually terminated after identifying an interpretable and highly accurate individual. The operators ' + ' , ' -' , ' × ' , ' / ' , 'ln_abs() ' (24)…”

Section: Domain Knowledge-guidedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Zhou

Yang

Xiao

et al. 2023

Chin. J. Mech. Eng.

View full text Add to dashboard Cite

show abstract

“…The mean function m(x) is set to be 0 for convenience. The kernel function is chosen as the squared exponential kernel, (17…”

Section: Bayesian Optimizationmentioning

confidence: 99%

“…However, the sufficient well-labelled data are usually expensive in many scenarios, especially for the high-fidelity fracture predictions [15,16]. Moreover, physics-informed neural networks (PINNs) have recently been implemented to overcome the low data availability [17]. PINNs assimilate physical governing equations into loss functions, which means PINNs are trained to satisfy the given training data as well as the imposed governing equations [18].…”

Section: Introductionmentioning

confidence: 99%

An auto-tuned hybrid deep learning approach for predicting fracture evolution

Sheng

Cheng

Yang

et al. 2022

Engineering with Computers

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In this study, a novel auto-tuned hybrid deep learning approach composed of three base deep learning models, namely, long short-term memory, gated recurrent unit, and support vector regression, is developed to predict the fracture evolution process. The novelty of this framework lies in the auto-determined hyperparameter configurations for each base model based on the Bayesian optimization technique, which guarantees the fast and easy implementation in various practical applications. Moreover, the ensemble modeling technique auto consolidates the predictive capability of each base model to generate the final optimized hybrid model, which offers a better prediction of the overall fracture pattern evolution, as demonstrated by a case study. The comparison of the different prediction strategies exhibits that the direct prediction is a better option than the recursive prediction, in particular for a longer prediction distance. The proposed approach may be applied in various sequential data predictions by adopting the adaptive prediction scheme.

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“…Instead of solving the PDEs directly, the DEM regards the potential energy of the system expressed in the local form based on classical continuum mechanics as the loss function, which has derivatives of a lower order compared to the strong form. Further, a length scale parameter in phase field is introduced to control the finite width of process zone and the fracture energy is considered in the loss function for fracture mechanical problems 52,53 . Nevertheless, additional variables and equations are introduced to represent the crack topology and mesh refinement is required at the vicinity of crack.…”

Section: Introductionmentioning

confidence: 99%

A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads

Zhou

2023

Numerical Meth Engineering

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In this paper, a nonlocal energy‐informed neural network is proposed to characterize the deformation behaviors of elastic solids with cracks subjected to thermomechanical loads in the framework of ordinary state‐based peridynamics. Based on principle of virtual work, a nonlocal energy approach is developed to recast the solution to peridynamic equilibrium equation as a problem of minimizing the potential energy of the system, which automatically satisfies the traction‐free boundary conditions. Meanwhile, the energy representation of physical system can be treated as the loss function for machine learning methods. Therefore, a nonlocal energy‐informed neural network is constructed to approximate the solution of the system. A distinct advantage of the proposed neural network is that the strain energy is expressed in terms of spatial integration instead of spatial derivatives, which avoids the invalidation of automatic differentiation at the crack surfaces in original physics‐informed neural networks. To demonstrate the convergence and accuracy of the proposed neural network, a series of problems in solid and fracture mechanics are conducted, and compared with results from analytical solutions or classical numerical methods. Additionally, for elastic material containing initial cracks, displacement extrapolation method is encoded into the proposed neural network to evaluate the static stress intensity factor.

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Physics-informed machine learning model for computational fracture of quasi-brittle materials without labelled data

Cited by 49 publications

References 34 publications

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

An auto-tuned hybrid deep learning approach for predicting fracture evolution

A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads

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