On the constitutive modeling of dual-phase steels at finite strains: a generalized plasticity based approach

In this work we propose a general theoretic framework for the derivation of constitutive equations for dual-phase steels, undergoing continuum finite deformation. The proposed framework is based on the generalized plasticity theory and comprises the following three basic characteristics: 1.A multiplicative decomposition of the deformation gradient into elastic and plastic parts. 2.A hyperelastic constitutive equation 3.A general formulation of the theory which prescribes only the number and the nature of the internal variables, while it leaves their evolution laws unspecified. Due to this generality several different loading functions, flow rules and hardening laws can be analyzed within the proposed framework by leaving its basic structure essentially unaltered. As an application, a rather simple material model, which comprises a von-Mises loading function, an associative flow rule and a non-linear kinematic hardening law, is proposed. The ability of the model in simulating simplified representation of the experimentally observed behaviour is tested by two representative numerical examples

On the constitutive modeling of dual-phase steels at finite strains: a generalized plasticity based approach

In this work we propose a general theoretic framework for the derivation of constitutive equations for dual-phase steels, undergoing continuum finite deformation. The proposed framework is based on the generalized plasticity theory and comprises the following three basic characteristics: 1.A multiplicative decomposition of the deformation gradient into elastic and plastic parts. 2.A hyperelastic constitutive equation 3.A general formulation of the theory which prescribes only the number and the nature of the internal variables, while it leaves their evolution laws unspecified. Due to this generality several different loading functions, flow rules and hardening laws can be analyzed within the proposed framework by leaving its basic structure essentially unaltered. As an application, a rather simple material model, which comprises a von-Mises loading function, an associative flow rule and a non-linear kinematic hardening law, is proposed. The ability of the model in simulating simplified representation of the experimentally observed behaviour is tested by two representative numerical examples

The scaled boundary finite element method for the efficient modeling of linear elastic fracture

In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM’s potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed

On the use of mode shape curvatures for damage localization under varying environmental conditions

A novel damage localization method is introduced in this study, which exploits mode shape curvatures as damage features, while accounting for operational variability. The developed framework operates in an output-only regime,that is, it does not assume availability of records from the influencing environmental/operational quantities but rather from response quantities alone. The introduced tool comprises 3 stages pertaining to training, validation, and diagnostics. During the training stage, a representation of the healthy, or baseline, structural state is acquired over varying operational conditions. A data matrix is formulated, whose individual columns correspond to mode shape curvatures at distinct operational conditions, and principal component analysis (PCA) is applied for extraction of the imprints of separate operational sources on these curvatures. To this end, a residual matrix between the original and the PCA mapped data is formed serving for statistical characterization of each mode. Subsequently, during the validation and diagnostics stages, the mode shape curvature matrices for the currently inspected structural state are assembled and the same PCA mapping is enforced. A typical hypothesis test and a corresponding damage index are then adopted in order to firstly detect damage, and to secondly localize damage, should this exist. The implementation of the proposed method in 2 numerical case studies confirms its effectiveness and the encouraging results suggest further investigation on operating structural systems. ISSN:1545-2255 ISSN:1545-226

Towards a multiscale scheme for nonlinear dynamic analysis of masonry structures with damage

In this work, a three dimensional multiscale formulation is presented for the analysis of masonry structures based on the multiscale finite element formulation. The method is developed within the framework of the Enhanced Multiscale Finite Element Method. Through this approach, two discretization schemes are considered, namely a fine mesh that accounts for the micro-structure and a coarse mesh that encapsulates the former. Through a numerically derived mapping, the fine scale information is propagated to the coarse mesh where the numerical solution of the governing equations is performed. Inelasticity is introduced at the fine mesh by considering a set of internal variables corresponding to the plastic deformation accumulating at the Gauss points of each fine-scale element. These additional quantities evolve according to properly defined smooth evolution equations. The proposed formalism results in a nonlinear dynamic analysis method where the micro-level state matrices need only be evaluated once at the beginning of the analysis procedure. The accuracy and computational efficiency of the proposed scheme is verified through an illustrative example

Hybridization of Guided Surface Acoustic Modes in Unconsolidated Granular Media by a Resonant Metasurface

We investigate the interaction of guided surface acoustic modes (GSAMs) in unconsolidated granular media with a metasurface, consisting of an array of vertical oscillators. We experimentally observe the hybridization of the lowest-order GSAM at the metasurface resonance, and note the absence of mode delocalization found in homogeneous media. Our numerical studies reveal how the stiffness gradient induced by gravity in granular media causes a down-conversion of all the higher-order GSAMs, which preserves the acoustic energy confinement. We anticipate these findings to have implications in the design of seismic-wave protection devices in stratified soils

A hysteretic multiscale formulation for validating computational models of heterogeneous structures

A framework for the development of accurate yet computationally efficient numerical models is proposed in this work, within the context of computational model validation. The accelerated computation achieved herein relies on the implementation of a recently derived multiscale finite element formulation, able to alternate between scales of different complexity. In such a scheme, the micro-scale is modelled using a hysteretic finite elements formulation. In the micro-level, nonlinearity is captured via a set of additional hysteretic degrees of freedom compactly described by an appropriate hysteric law, which gravely simplifies the dynamic analysis task. The computational efficiency of the scheme is rooted in the interaction between the micro- and a macro-mesh level, defined through suitable interpolation fields that map the finer mesh displacement field to the coarser mesh displacement field. Furthermore, damage related phenomena that are manifested at the micro-level are accounted for, using a set of additional evolution equations corresponding to the stiffness degradation and strength deterioration of the underlying material. The developed modelling approach is utilized for the purpose of model validation; firstly, in the context of reliability analysis; and secondly, within an inverse problem formulation where the identification of constitutive parameters via availability of acceleration response data is sought

Hybridization of Guided Surface Acoustic Modes in Unconsolidated Granular Media by a Resonant Metasurface

We investigate the interaction of guided surface acoustic modes (GSAMs) in unconsolidated granular media with a metasurface, consisting of an array of vertical oscillators. We experimentally observe the hybridization of the lowest-order GSAM at the metasurface resonance, and note the absence of mode delocalization found in homogeneous media. Our numerical studies reveal how the stiffness gradient induced by gravity in granular media causes a down-conversion of all the higher-order GSAMs, which preserves the acoustic energy confinement. We anticipate these findings to have implications in the design of seismic-wave protection devices in stratified soils

A Discontinuous Unscented Kalman Filter for Non-Smooth Dynamic Problems

For a number of applications, including real/time damage diagnostics as well as control, online methods, i.e., methods which may be implemented on-the-fly, are necessary. Within a system identification context, this implies adoption of filtering algorithms, typically of the Kalman or Bayesian class. For engineered structures, damage or deterioration may often manifest in relation to phenomena such as fracture, plasticity, impact, or friction. Despite the different nature of the previous phenomena, they are described by a common denominator: switching behavior upon occurrence of discrete events. Such events include for example, crack initiation, transitions between elastic and plastic response, or between stick and slide modes. Typically, the state-space equations of such models are non-differentiable at such events, rendering the corresponding systems non-smooth. Identification of non-smooth systems poses greater difficulties than smooth problems of similar computational complexity. Up to a certain extent, this may be attributed to the varying identifiability of such systems, which violates a basic requirement of online Bayesian Identification algorithms, thus affecting their convergence for non-smooth problems. Herein, a treatment to this problem is proposed by the authors, termed the Discontinuous D– modification, where unidentifiable parameters are acknowledged and temporarily excluded from the problem formulation. In this work, the D– modification is illustrated for the case of the Unscented Kalman Filter UKF, resulting in a method termed DUKF, proving superior performance to the conventional, and widely adopted, alternative

Online Bayesian Identification of Non-Smooth Systems

The robustness of online Bayesian Identification algorithms has been illustrated for a wide range of physical problems. The successful convergence of such algorithms for problems of highly nonlinear nature is tied to the precision of the approximation of the observed system via the employed state-space model. More sophisticated approximations, result in an increase of both the convergence rate and the associated computational cost. Nonetheless, the latter is a price worth paying for ensuring the former in the case of highly nonlinear problems. The assumption placed by most Bayesian filtering algorithms is that the parameters to be estimated are identifiable at each updating step. This however is a property that does not necessarily hold for systems involving non-smooth nonlinearities, i.e., systems whose state-space or measurement equations are not differentiable. Such systems are linked to the modelling of damage-related phenomena such as plasticity, impact and sliding amongst other. Hence, a separate approach is proposed herein, namely the modification of algorithms to account for the lack of identifiability encountered for parameters of a non-smooth system at a specific step. This modification is termed by the authors as, the Discontinuous, D- modification and relies on the idea that unidentifiable parameters should remain invariant in the corresponding updating steps. This work will illustrate the benefits of the D- modification on the convergence of the Unscented Kalman Filter for non-smooth problems. An example from the dynamics of rocking bodies will be used to demonstrate the advantages of the method