The MS focuses on the process of modeling, quantifying and estimating the effects of uncertainties that characterize irreversible/dissipative material behavior in quasi-static and dynamic conditions. Particular examples of great significance include metal fatigue and concrete fracture analysis, as well as material aging of bone tissues. Moreover, special attention will be paid to the multi-scale and multi-fidelity nature of these problems, as well as to Bayesian analysis and corresponding design of experiments. Numerical tools to be discussed are low-rank functional approximations, Bayesian learning, optimization, stochastic Galerkin, polynomial chaos expansion, and stochastic homogenization, to name just a few.
16:30
Stochastic multiscale analysis of nonlinear dissipative phenomena
Bojana Rosic | University of Twente | Netherlands
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Authors:
Bojana Rosic | University of Twente | Netherlands
Muhammad Sadiq Sarfaraz | TU Braunschweig | Germany
Sharana Kumar Shivanand | TU Braunschweig | Germany
The behavior of materials produced by modern manufacturing processes is not fully predictive. The predictability and control of the process are both jeopardized by material anisotropy and heterogeneity in the microstructure, as well as by the presence of defects arising during additive production. In order to reliably predict the macroscopic deformation, the micro- and meso-scale material description has to be considered from a probabilistic point of view. However, this gives rise to the high-dimensionality of the computational problem mathematically described by variational inequalities.The main goal of this talk is to show how to build an online low-rank and sparse approximation of the lower-scale models, which are then efficiently propagated to the upper-scale ones in a full functional approximation form.
17:00
Domain decomposition for random perforated domains
Robert Gruhlke | WIAS Berlin | Germany
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Authors:
Robert Gruhlke | WIAS Berlin | Germany
Martin Eigel | WIAS Berlin | Germany
In this talk we consider elliptic PDEs defined on randomly perforated domains. Under the assumption of isolated perforations, any perforation is characterised by a set of parameters determining e.g. shape and location. We construct a hybrid domain decomposition approach based on multiple surrogates of the involved local parameter dependent discrete Poincaré-Steklov operators, for instance approximated in hierarchical tensor formats for artificial neural networks. The developed method allows for a fast propagation of random geometric input to output quantities of interest.
17:30
Modelling fatigue crack initiation in metallic specimens by spatial Poisson processes
Zaid Sawlan | KAUST | Saudi Arabia
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Authors:
Zaid Sawlan | KAUST | Saudi Arabia
Ivo Babuska | ICES, University of Texas | United States
Barna Szabo | ESRD | United States
Raul F. Tempone | RWTH Aachen and KAUST | Germany
Marco Scavino | KAUST | Saudi Arabia
Predicting fatigue in mechanical components is extremely important for preventing hazardous situations. In this work, we propose a stochastic model to predict the crack initiations on the surface of metallic components under cyclic loading. The stochastic model is based on spatial Poisson processes with intensity function that combines stress-life (S-N) curves with an averaged effective stress function. The stress function is computed after solving numerically the linear elasticity equations on the specimen domains using finite element methods. For the S-N curves, we consider fatigue-limit and random fatigue-limit models. The rate function of the Poisson process is suitably scaled by a parameterized highly stressed volume. The resulting model can predict the initiation of cracks in specimens made from the same material with new geometries.
18:00
An uncertainty assessment framework for diffusive transport in biobased hydrogels
Davide Baroli | Aachen Institute for Advanced Study in Computational Engineering Science | Germany
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Authors:
Davide Baroli | Aachen Institute for Advanced Study in Computational Engineering Science | Germany
Stephane Bordas | University of Luxembourg | Luxembourg
Anti Paajanen | VTT Technical Research Centre of Finland Ltd | Finland
Karen Veroy-Grepl | Eindhoven University of Technology (TU/e) | Netherlands
The assessment of uncertainty propagation is one of the main challenges in computational materials design. It is especially relevant for studies on soft matter systems, which tend to exhibit microstructural heterogeneity. In this work, we propose a numerical framework for predicting the diffusive transport properties of biobased hydrogels, and the propagation of uncertainty due to a limited knowledge of their microstructure. The framework uses Langevin dynamics simulation to determine molecular diffusivity as a function of density, and a finite element formulation to predict diffusive transport on the microstructural level. The uncertainty in the microscale diffusivity is described by a zero mean Gaussian random field, which is obtained by solving a Matern-PDE based equation. To alleviate the curse-of-dimensionality, a polynomial chaos approximation based on Leja-nested grid is adopted. The numerical results are tested on 3D cylindrical geometry, assessing the propagation of uncertainty within the multiscale framework.