A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials - Application to Uniaxial Cyclic Response of Concrete

In complex materials, numerous intertwined phenomena underlie the overall response at macroscale. These phenomena can pertain to different engineering fields (mechanical , chemical, electrical), occur at different scales, can appear as uncertain, and are nonlinear. Interacting with complex materials thus calls for developing nonlinear computational approaches where multi-scale techniques that grasp key phenomena at the relevant scale need to be mingled with stochastic methods accounting for uncertainties. In this chapter, we develop such a computational approach for modeling the mechanical response of a representative volume of concrete in uniaxial cyclic loading. A mesoscale is defined such that it represents an equivalent heterogeneous medium: nonlinear local response is modeled in the framework of Thermodynamics with Internal Variables; spatial variability of the local response is represented by correlated random vector fields generated with the Spectral Representation Method. Macroscale response is recovered through standard ho-mogenization procedure from Micromechanics and shows salient features of the uniaxial cyclic response of concrete that are not explicitly modeled at mesoscale.Comment: Computational Methods for Solids and Fluids, 41, Springer International Publishing, pp.123-160, 2016, Computational Methods in Applied Sciences, 978-3-319-27994-

Diffusion maps-aided Neural Networks for the solution of parametrized PDEs

This work introduces a surrogate modeling strategy, based on diffusion maps manifold learning and artificial neural networks. On this basis, a numerical procedure is developed for cost-efficient predictions of a complex system's response modeled by parametrized partial differential equations. The idea is to utilize a collection of solution snapshots, obtained by solving the partial differential equation for a small number of parameter values, in order to establish an efficient yet accurate mapping from the problem's parametric space to its solution space. In common practice, solving the partial differential equations in the framework of the finite element method leads to high-dimensional data sets, which are a major challenge for machine learning algorithms to handle (curse of dimensionality). To overcome this problem, the proposed method exploits the dimensionality reduction properties of the diffusion maps algorithm in order to obtain a meaningful low-dimensional representation of the solution data set. With this approach, a reduced set of typerparameters' is obtained, namely, the diffusion map coordinates, that characterize the high-dimensional solution vectors. Using this reduced representation, a feed-forward neural network is efficiently trained that maps the problem's parameter values to their images in the low-dimensional diffusion maps space. This approach offers two advantages. The obvious one is that it reduces the computational resources and CPU time needed to train the neural network, which can be prohibitive for high dimensional problems. The second advantage is that training the neural network on the diffusion map coordinates, essentially translates to using the diffusion maps distance in the MSE loss function of the network. Compared to the Euclidean distance in the ambient space, the diffusion distance gives a better approximation of the distance between two points on the solution manifold, which leads to a more accurate network. Lastly, a mapping is developed based on the Laplacian pyramids scheme in order to convert points from the diffusion maps space back to the solution space. The composition of the neural network with the Laplacian pyramid scheme, substitutes the process of solving the partial differential equation under consideration, and is capable of providing the additional system solutions at a very low cost and high accuracy. (C) 2020 Elsevier B.V. All rights reserved

A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling

International audienceA stochastic data-driven multilevel finite-element (FE2) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data. Then, a FE2 method replacing the nonlinear multiscale calculations by the NN–I is developed. The NN–I scheme improved the accuracy of the neural-network surrogate model when insufficient data were available. Due to the achieved reduction in computational time, which was several orders of magnitude less than that to direct FE2, the use of such a machine-learning method is demonstrated for performing Monte Carlo simulations in nonlinear heterogeneous structures and propagating uncertainties in this context, and the identification of probabilistic models at the macroscale on some quantities of interest. Applications to nonlinear electric conduction in graphene–polymer composites are presented

Computational Methods in Stochastic DynamicsVolume 2 /

XVI, 356 p.online resource

Στοχαστική Ανάλυση Αλληλεπίδρασης Εδάφους-Θεμελίου

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Δομοστατικός Σχεδιασμός και Ανάλυση των Κατασκευών

Reliability analysis of structures under seismic loading

Summarization: The objective of this paper is to perform reliability analysis of space frames under seismic loading. In order to produce the dynamic loads a number of random accelerograms is produced from the elastic design response spectrum of the region. Structural reliability analysis is performed using the Monte Carlo Simulation (MCS) method. The results obtained for a realistic structural problem indicate the applicability of the proposed procedure.Παρουσιάστηκε στο: Fifth World Congress on Computational Mechanic

A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites

International audienc