Numerical issues in distributed inelasticity modelling of rc frame elements for seismic analysis

Student: Armando Calabrese
Supervisors: Dr Rui Pinho


Distributed inelasticity elements are becoming widely employed in structural engineering applications, either for research or professional engineering purposes, due to their inherent advantages in representing frame elements. More specifically, distributed inelasticity elements (i) allow the inelastic behaviour to spread throughout the entire element (ii) do not require any calibration of their parameters against the response of an actual or ideal frame element under idealized loading conditions.

Particular distributed inelasticity formulations are the ones commonly referred as "fibre models", where the cross-section of the element is represented by a number of fibres, each one associated with a uniaxial stress-strain relationship. Such models feature additional assets, which can be summarized as: no requirement of a prior moment-curvature analysis of members; no need to introduce any element hysteretic response (as it is defined by the material properties); direct modelling of axial load-bending moment interaction (both on strength and stiffness); straightforward representation of biaxial loading and interaction between flexural strength in orthogonal directions.

Basically, distributed inelasticity frame elements can be implemented with two different finite elements (FE) formulations. The classical Displacement-Based (DB) ones, in which the displacement field is imposed, are giving the lead to the more recent Force-Based (FB) approaches, where the equilibrium is strictly satisfied and no restraints are placed to the development of inelastic deformations throughout the member. For this reason, FB formulations are extremely appealing for earthquake engineering applications, where significant material nonlinearities are expected to occur. Both DB and FB elements, however, produce non-objective results in case of members with softening sectional behaviour, such as reinforced concrete (RC) frame elements subjected to high axial load ratio. This numerical issue is commonly known as "Strain localization", or simply "Localization". The same expression is also used in damage mechanics to indicate the similar problem of concentration of deformations which is physically observed when testing concrete specimens. While this dissertation mainly investigates the analytical issues, the experimental features are discussed as well, in order to provide a clearer perception of some difficulties that can be faced when modelling RC degrading behaviour. Moreover, the definition and control of the strain and curvature limits, which are associated with the empirical definition of RC properties, is essential to interpret and validate the results of a model of any kind of structure.

You may download a digital version of this MSc dissertation here.