Computational modelling of fibre-reinforced cementitious composites: An analysis of discrete and mesh-independent techniques
Failure patterns and mechanical behaviour of high performance fibre-reinforced cementitious composites depend to a large extent on the distribution of fibres within a specimen. A discrete treatment of fibres enables us to study the influence of various fibre distributions on the mechanical properties of the material. The numerical analysis of large numbers of arbitrarily distributed discrete thin fibres embedded in a continuum is how- ever a computationally demanding process. In this work, two different methodologies are proposed to model discrete fibres embedded in a continuum matrix. To ensure numerical efficiency, fibres are not explicitly discretized but they are superposed to a background mesh representing the continuous matrix material.
In the first approach, the fibre-force approach, fibres are modelled by applying discrete forces to the background mesh. The background mesh represents the matrix while the discrete forces represent the interaction between fibres and matrix. These forces are assumed to be equal to fibre pull-out forces. With this approach, experimental data or micro mechanical models, including detailed information about the fibre-matrix interface, can be directly incorporated into the model.
The second approach is based on the partition of unity property of finite element shape functions. The handling of discrete thin fibres embedded in the continuum matrix is made possible by a special enrichment function that represents the action of each fibre on the matrix. The constitutive behaviour of the matrix material, the fibre material and the fibre-matrix bond can be defined independently. In contrast to the fibre-force approach, the interaction between matrix and fibres is defined through the constitutive relation describing the bond-slip at the fibre interface. In both approaches the interaction of the fibres and a damaged matrix material is investigated. The partition of unity based approach is applied to experiments taken from literature. In addition to modelling of fibre-reinforced concrete, this approach is applied to concrete reinforced with rebars and with rebars and fibres. The comparison to available experimental results shows that the proposed methodology is able to capture the basic behaviour of the materials but indicates the need for an extension to three dimensions to represent the material behaviour in a realistic fashion.
Both proposed approaches basically solve the initially posed problem to model discrete fibres embedded in a continuum without including the fibres into the finite element mesh.