Complex Dynamical Behavior in the Shear‐Displacement Model for Bulk Metallic Glasses during Plastic Deformation

Chen, Cun; Guan, Shaokang; Zhang, Liying

doi:10.1155/2018/7643762

Cited by 4 publications

(3 citation statements)

References 34 publications

(66 reference statements)

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“…e stick-slip system shows rich dynamic behaviors such as chaos and quasi periodic solution [16,17]. In this paper, we prove that there is a periodic solution based on mathematical theory, and the periodic solution is accordant with the sinusoidal density variations in shear bands [18].…”

Section: Conclusion and Discussionmentioning

confidence: 65%

Plastic Dynamical Model for Bulk Metallic Glasses

Yao

Cheng

2019

Complexity

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Based on previous experimental results of the plastic dynamic analysis of metallic glasses upon compressive loading, a dynamical model is proposed. This model includes the sliding speed of shear bands in the plastically strained metallic glasses, the shear resistance of shear bands, the internal friction resulting from plastic deformation, and the influences from the testing machine. This model analysis quantitatively predicts that the loading rate can influence the transition of the plastic dynamics in metallic glasses from chaotic (low loading rate range) to stable behavior (high loading rate range), which is consistent with the previous experimental results on the compression tests of a Cu50Zr45Ti5 metallic glass. Moreover, we investigate the existence of a nonconstant periodic solution for plastic dynamical model of bulk metallic glasses by using Manásevich–Mawhin continuation theorem.

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Section: Conclusion and Discussionmentioning

confidence: 65%

Plastic Dynamical Model for Bulk Metallic Glasses

Yao

Cheng

2019

Complexity

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“…This spring-block model could be related to transform faults, and it is also meaningful note that the research on such kind of spring-block Burridge-Knopoff model can provide useful clues for observed phenomena in seismology [31], which is the key to solve the scientific problem of whether earthquakes can be predicted or transformed. Meanwhile, the present work also provides a reference for the problem of plastic deformation in disordered materials, which is related to a spring-block model [36][37][38][39]. Some experts studied the damage process and discussed a discrete model based on the potential energy of the block system [40][41][42].…”

Section: Resultsmentioning

confidence: 99%

Complex Dynamical Behaviors in a Spring‐Block Model with Periodic Perturbation

Chen

Ren

2019

Complexity

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A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic solutions, chaotic solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics.

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“…If there is a slow driving force, the system crackles accompanied with various sizes of discrete events, such as the earthquakes burst at a critical state as the tectonic plates interacting with each other under a driving plate [3], [4]; We have explored the plastic deformation mechanism during compressive deformation for disordered materials such as bulk metallic glasses (BMGs) and highentropy alloy and give stress-strain signals prediction [5]- [7]. The serrated flow in plastic dynamics manifests self-organization critical (SOC) state [8]- [12]. The intermittent serrated flow burst in the disordered materials during plastic deformation is induced by the interaction of the shear bands, which manifests as different size of sliding events [13].…”

Section: Introductionmentioning

confidence: 99%

The System Identification and Prediction of the Social Earthquakes Burst in Human Society

et al. 2020

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The internal mechanism of the social "earthquakes"-the wars burst in human society, is investigated by nonlinear theory. We explore the scaling behavior in the human activity and the historical evolution of ancient China. Based on the war chronology and history chronology from B.C.2000 to A.D.1840, using statistical analysis together with the detrended fluctuation analysis, we find that the social evolution system shows self-organized critical behavior and there exists self-similar scaling behavior during the evolution system. Based on time-delay reconstructed phase space, a modified radial basis function neural network (modified RBF-NN) is used to predict the number of wars and the transformation of the historical stage. It shows that the prediction result matches quite well with the real value for the following two historical stages. Furthermore, by singular value decomposition and the sparse identification algorithm in time-delay coordinates, the coefficients of the candidate functions in identified system can be solved from a sparse regression problem. We extracted the governing equations of big events burst in social system. The identified system fits well with the real data, and it can capture the same topology with the original system of wars. In this paper, we investigated the wars burst in social system by statistic analysis, neural network as well as sparse identification. It sheds light on the study of wars or conflicts from perspective of data science and dynamical theory. INDEX TERMS Scaling behavior, Self-organized criticality, Neural networks, System identification.

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Complex Dynamical Behavior in the Shear‐Displacement Model for Bulk Metallic Glasses during Plastic Deformation

Cited by 4 publications

References 34 publications

Plastic Dynamical Model for Bulk Metallic Glasses

Plastic Dynamical Model for Bulk Metallic Glasses

Complex Dynamical Behaviors in a Spring‐Block Model with Periodic Perturbation

The System Identification and Prediction of the Social Earthquakes Burst in Human Society

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