References of "Paladim, Daniel-Alves"
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See detailGuaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales
Paladim, Daniel-Alves; de Almeida, José Paulo Baptista; Bordas, Stéphane UL et al

in International Journal for Numerical Methods in Engineering (2017), 110(2), 103132

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion ... [more ▼]

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. We typically consider linear elliptic diffusion problems in randomly packed particulate composites. Our work extends the pioneering work presented in [26,32] in order to bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic, and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager-Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss-Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation. [less ▲]

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See detailMulti-scale methods for fracture: model learning across scales, digital twinning and factors of safety
Bordas, Stéphane UL; Beex, Lars UL; Kerfriden, Pierre et al

Scientific Conference (2015, November 18)

Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel  Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety ... [more ▼]

Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel  Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre breakage, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mechanisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary.  We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of fracture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the “factors of safety” era. [less ▲]

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