Task 2

Cohesive fracture models for the analysis of concrete structures

Object

The first objective of Task 2 is the development and assessment of hybrid and mixed finite element formulations for cohesive fracture analysis of concrete structures. The second objective consists in the study and implementation of adequate transition techniques to move from a pure continuum approach based on the use of damage mechanics models to a discrete approach where a cohesive crack is introduced in the direction of the localization band. This task supports one doctoral programme, scheduled to start at the beginning of 2007. (top)

Motivation

In recent years the research group has been involved in the development of continuum damage models based on the use non-conventional hybrid and mixed finite element formulations [93-95,99-103,106]. These models are adequate to capture the response of concrete structures at early stages of loading, characterized by diffuse micro-cracking. However, for increasing loading conditions, those micro-cracks may coalesce to create only a few macro-cracks. In this case, the best numerical choice corresponds to the use of cohesive crack models [9-12]. To make possible the simulation of the complete fracture process of concrete structures based on the use non-conventional finite element formulations, it is necessary to complement the continuum damage models already implemented with cohesive crack models. The transition techniques that allow for the combination of both the continuum and the discrete approaches [14-16] have also to be studied and implemented. (top)

Current results

One of the main features of the hybrid-mixed finite element formulations is the possibility of enriching the approximation basis with special purpose functions. Consequently, functions modelling directly the displacement discontinuity and stress singularities may be included [153-154].

The numerical modelling of cohesive crack process ranges from confining the propagation to inter-element boundaries [109-111,155-156] to allowing propagation through the elements [112-116], to minimize the need of remeshing operations and to enhance the use of coarser meshes. Different numerical modelling techniques are currently used namely the Extended Finite Element Method [118-124], the Generalised Finite Element Method [125-131] and enhanced strain elements [157].

The external consultant, Prof. S. Proença has a relevant experience in this field [125,127,128,137]. (top)

Proposed developments

The research activity will focus on two main topics: the development of hybrid and mixed finite element formulations for cohesive crack analysis and the implementation of adequate transition techniques to combine the continuum and discrete approaches. The efficiency and accuracy of meshless methods [145,146] in cohesive crack modelling will be assessed. (top)

Methodology

The new formulations will be based in the cohesive crack model presented in [122]. In the description of the constitutive relations, the bulk material is assumed to be linear elastic and a simple mixed-mode cohesive model is assumed for the material in the processing zone, under predominantly tensile states of stress.

Non-conventional hybrid and mixed finite element formulations will be the main supporting numerical tools to be used in the development of the 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. The numerical procedure to be developed consists in taking a relatively coarse hybrid-mixed finite element mesh and to enrich the approximation with a moving basis of crack solutions to model propagation. The moving basis is defined at mesh level to make possible the modelling of the propagation of the fracture process in the domain and across the boundaries of the elements.

The definition of the proper time and location for the occurrence of the transition from continuum to discrete approaches is still an open question. A second important issue concerning the transition is the definition of the properties of the cohesive crack originating from the continuum model at the moment of the transition. One interesting approach to be followed is defined by Comi and co-authors in [15,18,119]. They define a critical damage and direction for the initiation of the discrete crack based on an analytical estimate of the bandwidth. More specifically, a crack is introduced in the direction of the localization band where the damage has reached a critical value. The traction-displacement discontinuity law for the new crack is defined in such a way that its fracture energy is equivalent to the residual energy to be dissipated within the localization band at the moment of the transition. (top)

Planning

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

The first two years will be devoted to the implementation and assessment of non-conventional models for cohesive crack propagation analysis. In the final year of the project, the transition techniques will be applied.

Both external consultants will be involved in Task 2. 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)