SIZE EFFECT IN LOCALISED FAILURE: TESTING, UNCERTAINTY, MODELLING

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Heterogeneous materials with a random composition - such as concrete, fibre-reinforced plastics, or geological materials, to name only a few - are nowadays prevalent in many engineering application areas. When loaded up to failure, the structures built of such materials exhibit a size effect together with a distinct softening behaviour due to the localization zone with dominant inelastic deformation.The first idea here is to develop an intrinsic localised failure model, starting with fine scale random materials with inclusions, such as concrete as an assembly of randomly placed aggregates surrounded by cement paste. The inclusions are often on a very small meso-scale, whereas the overall response has to be considered at a macro-scale, where the meso-scale cannot be resolved. Moreover, testing in the lab is typically performed with a small specimen with a very different scale than the one of a real, massive structure. Therefore, the full experimental validation on real-size structure is ruled out. Hence the predictive model development calls for a multiscale approach, where the computational models at the different scales will be coupled.The second idea here, given that the composition of the materials is considered random, is to develop probabilistic models that can capture the size effect; the Bayesian updating methods will be used to transfer the probabilistic information between different scales. In short, laboratory experiments and/or corresponding computations at fine scale can be used to update the material parameters defined as random fields for the models used at structural scale, keeping track of the size effect. The Bayesian methods effectively transform the ill-posed inverse problem of parameter identification, especially for this difficult multi-scale situation, into a well-posed direct problem of computing the model parameter probability distribution.Two composite materials with great application potential will be examined: the first pertains to cement-based fibre reinforced (CBFR) composites, and the second to 3D carbon fibre reinforced polymers (CFRP), also known as woven composite. The source of uncertainty for each material at fine scale, which pertains to geometry aspects, can be used to define the probability distribution of coarse scale material parameters. For each of these materials we can also provide full validation against experiments, such as the recently completed experimental program in the French excellence project ECOBA for CBFR and experimental results provided by the Centre for Composites Testing at Université de Technologie Compiègne.