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SIZE EFFECT IN LOCALISED FAILURE: TESTING, UNCERTAINTY, MODELLING

Subject Area Applied Mechanics, Statics and Dynamics
Materials in Sintering Processes and Generative Manufacturing Processes
Mechanical Properties of Metallic Materials and their Microstructural Origins
Term from 2016 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 316704785
 
Final Report Year 2022

Final Report Abstract

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, structures built of such materials exhibit a size effect—the specific strength decreases with the size—together with a distinct softening behaviour due to localisation zones with dominant inelastic deformation. The original aim of the project was to improve the understanding of size effects in failure of such inhomogeneous materials. The first objective here was to develop an intrinsic localised failure model, starting with fine scale random materials with possible inclusions, such as concrete as an assembly of randomly placed aggregates surrounded by cement paste. The inclusions or other random variations in material are often on a very small micro-/meso-scale, whereas the overall response has to be considered at a macro-scale, where this meso-scale cannot be computationally resolved. Moreover, testing in the lab is typically performed with a small size specimen with very different scale from the one of a real, massive structure. Therefore, the full experimental validation on real-size structures is typically ruled out. Hence the predictive model development calls for a multiscale approach, where the computational models at the different scales will be coupled. In a first step, ways how to include stochastic fine scale models into global scale simulations while obeying usual computational capacity limitations were examined. The multiscale coupling is achieved through the so-called mesh-in-element (MIEL) scale coupling, where compatibility for otherwise incompatible discretisations is weakly enforced with the help of local Lagrange multipliers. This kind of multiscale coupling can preserve size relations and thus account for the size effect. Such computations turn out to be a kind of coupled or co-simulations, where different models—here models at different scales and different stochastic realisations—run simultaneously (on-line) and interchange information. Still, these are coupled stochastic models, and can be very costly to run for large structures. Therefore ways to facilitate the upscaling in an off-line fashion were sought, i.e. before the simulation of the macro-scale structure. This is an idea which originally comes from the homogenisation of periodic structures. Thus the second objective was, given that the composition of the materials is considered random, to develop models that are probabilistic or stochastic and capture a size effect; Bayesian updating methods were used to transfer the probabilistic information between different scales, where reversibly stored energy and irreversibly dissipated energy are the main transfer quantities, thus ensuring thermodynamic consistency. In short, laboratory experiments and/or corresponding computations at fine scales 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 stochastic multi-scale situation, into a well-posed direct problem of computing the model parameter probability distributions. A further development was to find ways to combine these two approaches, the online direct stochastic multiscale coupling and the off-line stochastic upscaling, so as to take advantage of their specific properties. The upscaled models would thus be used in a large portion of a full-size structural model, and only where these upscaled models are not accurate enough one switches to a full on-line direct stochastic multiscale coupling be used, quasi a “magnifying lens” with more resolution power for localised failure zones, coupled to the overall off-line stochastic upscaled model. Thus a third objective was to find computational indicators for this kind of switching. Several such indicators based on machine learning with deep artificial neural networks have been investigated.

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