Thermodynamic admissibility of Bouc-Wen type hysteresis models

International audienceStarting from the relationship between the Bouc model and the endochronic theory and by adopting some new intrinsic time measures, the thermodynamic admissibility of the Bouc-Wen model is proved, in the univariate case as well as in the tensorial one. Moreover, the proposed proof encompasses the cases where a strength degradation term appears

A non-linear hardening model based on two coupled internal hardening variables: formulation and implementation

An elasto-plasticity model with coupled hardening variables of strain type is presented. In the theoretical framework of generalized associativity, the formulation of this model is based on the introduction of two hardening variables with a coupled evolution. Even if the corresponding hardening rules are linear, the stress-strain hardening evolution is non-linear. The numerical implementation by a standard return mapping algorithm is discussed and some numerical simulations of cyclic behaviour in the univariate case are presented

How to retrieve the normal modes using the POD

International audienceProper orthogonal decomposition (POD) is an increasingly popular way to analyze data, and to obtain either a low- dimensional approximated description of a high-dimensional process, or useful information for damage assessment. In the case of a dynamic system with n degrees of freedom, the purpose of POD is to retrieve the modal properties from the measured response. Until now, POD has been used for systems with a diagonal mass matrix. The aim of this presentation is double: first, to demonstrate that POD can also be used for a non-diagonal symmetric mass matrix; and second, to present sufficient conditions on the response sampling, in order to retrieve the modal characteristics with a prescribed accuracy. The conditions to obtain this approximation with a given accuracy are first explicitly given for the case without damping. Then the case of proportional damping is addressed and similar conditions are shown. The critical case of two modal frequencies close together is also studied, given that it requires particular conditions. The obtained conditions show that the expected accuracy is explicitly limited by the damping ratio. Some numerical tests illustrate the accuracy evolution of the approximated normal modes obtained by this method, with respect to the variation of the observation time and the damping ratio. This careful analysis can be useful for finding the cause of poor approximation properties in more complex cases, such as analysis of variation in nonlinear normal modes

Damage assessment of pre-stressed structures: A SVD-based approach to deal with time-varying loading

International audienceVibration-based methods are well-established and effective tools to assess the health state of civil, mechanical and aerospace engineering structures. However, their reliability is still affected by the variability of the features commonly used for damage detection. Environmental effects and changes in operational conditions are the main sources of variability in the structural response. As a consequence, the modal identification used to extract damage sensitive features has to face constricting requirements in terms of signals stationarity and performance accuracy. Moreover, with reference to the damage assessment, large variations of monitored features mask subtle effects due to damage, which remain undetected. This study is conceived to address both these issues by focusing, in particular, on the non-stationarity of the loading conditions of tensioned structures, such as cables and pre-stressed beams. The capability of spectral methods to deal with the modal identification of non-stationary systems is enhanced by a curve-fitting procedure based on nonlinear least squares optimization. Wavelet analysis is applied for comparison and validation of the FFT-based technique. Identified natural frequencies are then used for the damage detection, exploiting the capacity of singular values decomposition to discriminate between damage-related events and the intrinsic non-stationary nature of the structural response. A reduced-order realization of the features set is performed to amplify changes not belonging to measurement variability but deriving from exogenous events, such as damage. The proposed methodology is validated by experimental analyses carried out on beams subjected to time-varying loading conditions in order to simulate the health monitoring of quasi and non-stationary systems

Application of the orthogonality principle to the endochronic and Mroz models of plasticity

A new description of the endochronic and the Mroz model is discussed. It is based on the definition of a suitable pseudo-potential and the use of the generalized normality assumption. The key-point of this formulation is the dependence of the pseudo-potentials on state variables

Pseudo-potentials and loading surfaces for an endochronic plasticity theory with isotropic damage

The endochronic theory, developed in the early 70s, allows the plastic behavior of materials to be represented by introducing the notion of intrinsic time. With different viewpoints, several authors discussed the relationship between this theory and the classical theory of plasticity. Two major differences are the presence of plastic strains during unloading phases and the absence of an elastic domain. Later, the endochronic plasticity theory was modified in order to introduce the effect of damage. In the present paper, a basic endochronic model with isotropic damage is formulated starting from the postulate of strain equivalence. Unlike the previous similar analyses, in this presentation the formal tools chosen to formulate the model are those of convex analysis, often used in classical plasticity: namely pseudopotentials, indicator functions, subdifferentials, etc. As a result, the notion of loading surface for an endochronic model of plasticity with damage is investigated and an insightful comparison with classical models is made possible. A damage pseudopotential definition allowing a very general damage evolution is given

Convex analysis and thermodynamics

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Pseudo-potentials and bipotential: a constructive procedure for non-associated plasticity and unilateral contact

International audiencePseudo-potentials are very useful tools to define thermodynamically admissible constitutive rules. Bipotentials are convenient for numerical purposes, in particular for non-associative rules. Unfortunately, these functionals are not always easy to construct starting from a given constitutive law. This work proposes a procedure to find the pseudo-potentials and the bipotential starting from the usual description of a non-associative constitutive law. This method is applied to different non-associative plasticity models such as the Drucker-Prager model and the non-linear kinematic hardening model. The same procedure allows one to obtain the pseudo-potentials of an endochronic plasticity model. The pseudo-potentials for the contact problem with dissipation are constructed using the same ideas. For all these non-associative constitutive laws a bipotential is then automatically deduced