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A summarizing description of a statistical modeling method partly based on earlier publications is given to predict the total loading and breaking process of fiber bundles generated by tensile tests. This method uses some types of idealized fiber bundles, the so-called fiber bundle cells (basic types: E, EH, ES, and ET) to model the structure of real fibrous structures. Using one of these bundle cells or a composite bundle made of some bundle cells connected in parallel, the expected value and standard deviation of the whole damage process of this bundle can be calculated up to the breakage of the last intact fiber during a mechanical test. As a new application the fracture process of unidirectional composite beam is modeled during the 3P bending test considering the beam is built up of elementary embeddedfiber layers considered as E-type fiber bundle cells in the first step. Formulae for calculating the expected value and standard deviation processes of the bent specimen are elaborated assuming that the fiber breakages determined the failure of layers.

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In the fibrous structures such as textiles and composites there are fibre assemblies exhibiting statistical bundle like behaviour. This paper presents a modelling method and software FibreSpace, based on a system of structuralised statistical fibre bundles, so called fibre bundle cells. These fibre bundle cells introduced before represent different idealised and typified fibre properties such as fibre shape, state of deformation, gripping as a connection with the vicinity, and the characteristic of force-transmitting and damage. With the help of the weighted parallel connection of the fibre bundle cells the mechanical behaviour and the damage process of real fibrous systems can be modelled as well as some structural properties or the strength data of single fibres can be determined by a fibre bundle cells model identified on the basis of measurements. The applicability of the fibre bundle cells method and modelling program developed is demonstrated by modelling the load and damage process of real textile structures and unidirectional composites during tensile or flexural test.

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