Recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network [Phys. Rev. Lett. 96, 238701 (2006)]. Essentially, this is a transformation from the time domain to the network domain, which allows for the dynamics of the time series to be studied via the organization of the network. In this paper, we focus on the deterministic chaotic Rössler time series and stochastic noisy periodic data that yield substantially different structures of the networks. In particular, we test an extensive range of network topology statistics, which have not be discussed in previous works, but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles. Our goal is to find out how they reflect and quantify different aspects of specific dynamics, and how they can be used to distinguish different dynamical regimes. For example, we find that the joint degree distribution appears to fundamentally characterize the spatial organizations of the cycles in phase space, and this is quantified via assortativity coefficient. We applied the network statistics to the electrocardiograms of a healthy individual and an arrythmia patient. Such time series are typically pseudoperiodic, but are noisy and nonstationary and degrade traditional phase-space based methods. These time series are, however, better differentiated by our network-based statistics.

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This paper deals with the prediction of ductile damage based on CDM approach fully coupled with advanced elastoplastic constitutive equations. This fully coupled damage model is developed based on the total energy equivalence assumption under the thermodynamics of irreversible processes framework with state variables. In this model, the damage evolution is enhanced by accounting for both stress triaxiality and Lode angle. The proposed constitutive equations are implemented into Finite Element (FE) code ABAQUS/Explicit through a user material subroutine (VUMAT). The material parameters are determined by the hybrid experimental-numerical method using various tensile and shear tests. Validation of the proposed model has been done using different tests of two aluminum alloys (Al6061-T6 and Al6014-T4). Through comparisons of numerical simulations with experimental results for different loading paths, the predictive capabilities of the proposed model have been shown. The model is found to be able to capture the initiation as well as propagation of macro-crack in sheet and bulk metals during their forming processes.