SUMMARYIn the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness‐based Rayleigh damping model. Copyright © 2013 John Wiley & Sons, Ltd.

International audienceIn this paper we develop the governing equations of the coupled damage-plasticity model, which is capable of representing the main mechanisms of inelastic behavior including irreversible plastic deformation, change of elastic response and the localized failure. We show in particular how such model should be implemented within the stress-based variational formulation, providing an important advantage for local computation of the internal variables, which thus remains very robust and even non-iterative for the case of linear hardening model. Several simple examples are presented in order to illustrate the kind of response the model can represent

This paper presents the physical formulation of a 1D material model suitable for seismic applications. It is written within the framework of thermodynamics with internal variables that is, especially, very efficient for the phenomenological representation of material behaviors at macroscale: those of the representative elementary volume. The model can reproduce the main characteristics observed for concrete, that is nonsymetric loading rate-dependent (viscoelasticity) behavior with appearance of permanent deformations and local hysteresis (continuum plasticity), stiffness degradation (continuum damage), cracking due to displacement localization (discrete plasticity or damage). The parameters have a clear physical meaning and can thus be easily identified. Although this point is not detailed in the paper, this material model is developed to be implemented in a finite element computer program. Therefore, for the benefit of the robustness of the numerical implementation, (i) linear state equations (no local iteration required) are defined whenever possible and (ii) the conditions in which the presented model can enter the generalized standard materials class-whose elements benefit from good global and local stability properties-are clearly established. To illustrate the capabilities of this model-among them for Earthquake Engineering applications-results of some numerical applications are presented.

International audienceRayleigh damping forces are commonly introduced in the numerical simulations of nonlinear structures run to assess structural performance in case of an earthquake. Their purpose is to account for energy dissipative mechanisms not otherwise explicitly represented in the model. When caused by interactions between the structure and its surrounding environment, energy dissipation is external to the structure, whereas it is internal when resulting from energy absorption mechanisms activated in the structure. In this paper, the concept of discrepancy forces is introduced in the framework of computational dynamics. Then, damping forces are presented as a model of these so-called discrepancy forces to represent internal energy dissipation. On the other hand, the discrepancy forces are identified from a set of experimental data recorded during shaking-table test of a ductile moment-resisting frame, which provides the rationale for a critical look into Rayleigh damping forces. It is in particular observed that, for the structure tested, the Rayleigh damping model used is inaccurate as a representation of the discrepancy forces. Besides, while the knowledge of the discrepancy forces allows for rationally discussing the capabilities of the inelastic structural model to represent the actual behavior of the structure, this is only possible to a limited extent with the Rayleigh damping model used