Task I

Continuum damage models for the analysis of concrete structures

Object

The objective of Task 1 is the study and implementation of effective numerical models for the physically non-linear analysis of concrete structures based on the use of continuum damage mechanics concepts. This task supports one doctoral programme, scheduled to start in the beginning of 2007. (top)

Motivation

The response of concrete structures to increasing loadings is characterized in the early stage by the spreading of micro-cracks in localized regions. These micro-cracks eventually coalesce to create only a few macro-cracks. To numerically simulate this behaviour, a continuum damage approach proves to be efficient in the first stage. In recent years, encouraging results have been obtained [92] by combining damage models with non-conventional hybrid and mixed finite element formulations [90-91]. The research group has been working with this type of formulations, knowing that some of their properties [97-98] may lead to the development of very effective and robust numerical tools, overcoming most of the drawbacks usually associated to the use of classical conforming finite element formulations.

The potential of these alternative formulations combined with continuum damage models is far from being fully exploited. This research task is designed to improve and to generalize the numerical models already implemented [93-95,99-103,106]. (top)

Current results

The research behind the results reported in [99-106] has been developed in the framework of a project already concluded (POCTI/ECM/33066/2001, Stress finite elements for concrete dams). The PhD thesis [92] presented by Mrs. Cristina Silva (SFRH/BD/9050/2002) discusses the most important outcomes of this research. The two most promising damage models are described in [135], where their relative performance is also assessed. They correspond to a hybrid-mixed stress formulation [100, 101], where the effective stress and the displacement fields in the domain of each element and the displacements on the static boundary are independently approximated, and a hybrid-displacement formulation [103, 106], where the displacements in the domain of each element and the stress field on the kinematic boundary are independently modelled. All approximations are defined as linear combinations of complete sets of orthonormal Legendre polynomials. Both implementations use the isotropic continuum damage model [65] and the regularization is ensured by the use of non-local integral models [57] where the strain energy release rate is adopted as the non-local variable. (top)

Proposed developments

The research activity will focus on four main topics: the improvement of the numerical performance of the models already developed, the study and implementation of damage and plasticity coupled models [44-48], the definition of damage models dealing with dynamic loadings [22, 136-137] and the generalization of the models developed for plane structures to allow the analysis of 3D problems. (top)

Methodology

Non-conventional hybrid and mixed finite element formulations will remain the main supporting numerical tools to be used in the development of the new models.

In the hybrid-mixed stress model, three fields are independently approximated [135]. The main advantages associated with this type of formulation correspond to the flexibility in the choice of the approximation functions [90-91] and the accuracy of the static fields resulting from the computations. In previous works [93-95], all approximations are defined as linear combinations of complete sets of orthonormal Legendre polynomials. In future implementations, alternative approximation functions will be tested, namely the complete sets of orthonormal wavelets defined on the interval [140,141]. An interesting approach to be explored corresponds to enrich the hybrid-mixed stress approximations by including regularized Heavisde functions [140] that are close to the exact localization modes.

As reported in [135], the hybrid displacement formulations are computationally more demanding than the hybrid-mixed stress models. To improve their performance, a strategy combining the use of hybrid and hybrid-Trefftz models can be implemented. In this case, hybrid-Trefftz [2000] displacement elements will be used to model the part of the structural domain where elastic linear behaviour can be assumed.

A new approach to be tested corresponds to the use of meshless techniques [141-144] to support the development of damage based models for the analysis of 2D concrete structures.

Special attention will be given to the Moving Least Squares [145] and to the Element-Free Galerkin [146] Methods. For the implementation of coupled damage and plasticity models [44-48], use will be made of the experience acquired by the research group in the development of hybrid-mixed stress models for the elastoplastic analysis of plane structures [98,147]. The development of damage models accounting for dynamic loadings [22, 136-137] will be based on the works presented in [148-152]. (top)

Planning

The new PhD student will start his research programme by studying the existing damage models based on the use of non-conventional formulations. After this first stage, a three month period at the Politectico di Milano will help him to launch the development of the new research with the support of the external consultant, Prof. C. Comi.

The first eighteen months will be devoted to the improvement of the existing models and to the development of coupled damage and plasticity models. In the second half of the project, damage models for the dynamic analysis of structures and for 3D problems will be implemented and tested.

Both external consultants will be involved in Task 1. Prof. S. Proença will visit Lisbon every year Prof. C. Comi will host the PhD student in Milano and will visit Lisbon during the second year of the project. (top)