Abstract

A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one
of them compares results obtained by using the proposed model with results of a laboratory test.
 

Abstract

When solving dynamic problems, it is necessary to define in some way the damping of the structure. Generally, a damping term that depends on the velocities is incorporated directly into the dynamic equilibrium equation. To do this, we define a structural damping matrix, such as Rayleigh's, which is quite difficult to estimate. Once the damping has been defined, the problem is solved as a linear elastic one, what enters in contradiction with the fact that a dissipative phenomenon is being treated. In this chapter, an alternative with greater conceptual basis is described, which considers the structural damping based on a viscoelastic constitutive models in which the stress depends in some way on the strain velocity. In this way, the term of structural damping arises directly in the dynamic equilibrium equation, where the properties of the materials can be determined through simple laboratory tests.