Towards robust viscoelastic-plastic-damage material model with different hardenings/softenings capable of representing salient phenomena in seismic loading applications

Abstract

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.

A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials—Application to Uniaxial Cyclic Response of Concrete

“…As it is a source of damping in reinforced concrete structures in seismic loading, which modeling is a challenging issue, modeling this hysteresis has been the focus of research work (see e.g. [28,17]). In [16], a simplified version of the stochastic multi-scale material model presented in this chapter has been developed with only the yield stress σ y being heterogenous and without damage-plasticity coupling.…”

Structural Seismic Fragility Analysis of RC Frame with a New Family of Rayleigh Damping Models

“…The inelastic structural model is based on a fiber frame element suitably implemented in the framework of a displacement-based formulation so that it can integrate the uniaxial concrete behavior law recently developed by the authors [17] and briefly presented in this section. This constitutive model is capable of Figure 2: Acceleration time history recorded on the shaking table during the test and corresponding elastic response spectrum with a critical viscous damping ratio of 5%.…”

“…4. Note that the constitutive law used here can handle different behavior in compression and tension, and can also reproduce a visco-elastic response (see [17] for a full description). Viscosity is not considered in this work and, for the sake of conciseness, we only focus on the compressive part of the behavior law in Fig.…”

“…Energy dissipation in phase 1 thus comes from the friction in the cracks that appeared when applying dead load and from many other mechanisms always present in mechanical systems. When used, visco-elasticity and constitutive laws with local hysteresis [27,17] in the structural model could account for these energy dissipation sources but a small amount of additional damping usually has to be added. For the RC frame considered in this work, a free-vibration test was carried out after dead load had been applied and a first modal damping ratio of 3.3% was measured [16].…”

“…Thus, even if the seismic demand is again as low as in phase 1, the energy dissipative mechanisms are different because of frictions in the cracks that appeared within phase 2 or at degraded bound between steel and concrete. Here again, visco-elasticity and behavior laws with local hysteresis [27,17] in the structural model could account for these damping sources, but it generally has to be completed by additional damping.…”