Constitutive modelling of fibre-reinforced brittle materials: Dissertation

Jyrki Kullaa

Research output: ThesisDissertationCollection of Articles


The tensile behaviour of brittle materials can be enhanced by fibres. The cracking stress may increase, but the main influence is higher ductility after cracking. In some cases the material may also exhibit multiple cracking and tensile strain hardening behaviour thereafter. A computational tool for analysing structures made of fibre-reinforced brittle materials was developed, starting from the micromechanical properties of fibres, matrix, and interface. The constitutive model is fairly general, including both single and multiple fracture, the fracture mode being either fibre rupture or pullout. The study is divided into three parts: First, the mechanics of a single fibre is analysed. Second, the statistical tensile behaviour is evaluated by taking all fibre locations and orientations into account. Third, the macromechanical constitutive relation is incorporated into a finite element program for structural analysis. The fundamental assumption in the single fibre analysis is the existence of a symmetry fibre within the matrix segment between cracks. This assumption enables the pullout analysis of a short fibre bridging several cracks. The strain energy of fibre and matrix, matrix fracture energy, fibre debonding energy, and frictional pullout energy are all included in the model. The theoretical value of the bond modulus was studied by means of the finite element method and dimensional analysis. Its value was found to be several orders of magnitude higher than the experimentally measured values reported in the literature. The macromechanical behaviour is derived from several single fibre analyses by integrating over all possible fibre locations and orientations. The fibre orientation introduces additional phenomena: number of fibres bridging the crack, snubbing effect at the fibre bending point, and matrix spalling. The snubbing effect increases the stress in the composite, while the other two have a decreasing effect. Matrix spalling considerably increases the crack width. The fundamental assumption is that the fibres carry axial stresses only. The result is a complete constitutive tensile relation of composite: stress-strain or stress-crack width curve, as well as a prediction of crack spacing. For the effects due to fibre orientation, a systematic experimental procedure should be developed. The tensile model was extended into two and three dimensions by using the finite element method with smeared and discrete crack concepts and a multi-surface plasticity theory. The statistical tensile relation represents the behaviour normal to the crack. Automatic generation of interface elements on an existing geometry was developed to facilitate the modelling of discrete cracks after smeared crack analysis. The increase in the peak load of flexural members due to fibres, as measured in experimental tests, could be reproduced, which supports the validity of the approach proposed in this study.
Original languageEnglish
QualificationDoctor Degree
Awarding Institution
  • Aalto University
  • Määttänen, Mauri, Supervisor, External person
Award date4 Sept 1998
Place of PublicationEspoo
Print ISBNs951-38-5252-0
Electronic ISBNs951-38-5253-9
Publication statusPublished - 1998
MoE publication typeG5 Doctoral dissertation (article)


  • fibre reinforcement
  • ductility
  • multiple cracking
  • micromechanics
  • composite materials
  • finite element analysis
  • construction materials


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