GRACM 2021: Fracture across space and time: a journey through multiscale methods, model order reduction and machine learning

Professor Bordas will give a talk the 07/07/21 from 2:45 pm to 3:15 pm at the 10th GRACM.

To register : click here

For the full program: click here

Abstract

Fracture across space and time: a journey through multiscale methods, model order reduction and machine learning

We review and connect in this paper two approaches to solve multi-scale fracture problems. Machine learning and model order reduction on the one hand and multi-scale methods on the other hand. 

We explain as didactically as possible how material complexity has led to the need for acceleration methods and discuss advances in model selection and error estimation for such problems. 

We show how model reduction/machine learning and standard multiscale methods both fails when dealing with localization problems occurring in fracture mechanics. 

We conclude by discussing the possibility of digital twins and make a parallel with medical simulation. 

 

Literature


A computational library for multiscale modeling of material failure
H Talebi, M Silani, SPA Bordas, P Kerfriden, T Rabczuk
Computational Mechanics 53 (5), 1047-1071

Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
P Kerfriden, P Gosselet, S Adhikari, SPA Bordas
Computer Methods in Applied Mechanics and Engineering 200 (5-8), 850-866

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics
P Kerfriden, O Goury, T Rabczuk, SPA Bordas
Computer Methods in Applied Mechanics and Engineering 256, 169-188

Local/global model order reduction strategy for the simulation of quasi-brittle fracture
P Kerfriden, JC Passieux, SPA Bordas
International Journal for Numerical Methods in Engineering 89 (2), 154-179

Molecular Dynamics/XFEM Coupling by a Three Dimensional Extended Bridging Domain with Applications to Dynamic Brittle Fracture
H Talebi, M Silani, S Bordas, P Kerfriden, T Rabczuk
International Journal for Multiscale Computational Engineering 11 (6), 527-541


Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization
O Goury, D Amsallem, SPA Bordas, WK Liu, P Kerfriden
Computational Mechanics 58 (2), 213–234

Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
LAA Beex, P Kerfriden, T Rabczuk, SPA Bordas
Computer Methods in Applied Mechanics and Engineering 279, 348–378


Statistical extraction of process zones and representative subspaces in fracture of random composite
P Kerfriden, KM Schmidt, T Rabczuk, SPA Bordas
International Journal for Multiscale Computational Engineering 11 (3), 253-287

Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales
D Alves Paladim, JP Moitinho de Almeida, SPA Bordas, P Kerfriden
International Journal for Numerical Methods in Engineering 110 (2), 103–132

What makes data science different? A discussion involving statistics2. 0 and computational sciences
C Ley, SPA Bordas
International Journal of Data Science and Analytics 6 (3), 167-175

Mathematical modelling and artificial intelligence in Luxembourg: Twenty PhD students to be trained in data-driven modelling
S Bordas, S Natarajan, A Zilian
ERCIM News 115, 39-40