242 citations · 1.2k across the 28 of their papers we have counts for
31 papers
A Bayesian Approach to Modeling Finite Element Discretization Error
Anne Poot, Pierre Kerfriden, Iuri Rocha +1
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where…
A graph-based probabilistic geometric deep learning framework with online enforcement of physical constraints to predict the criticality of defects in porous materials
Vasilis Krokos, Stéphane P. A. Bordas, Pierre Kerfriden
Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (C…
Local uncovering of unresolved physics in structural mechanics: seamless choice of modelling resolution using a CutFEM level-set approach
Ehsan Mikaeili, Pierre Kerfriden, Susanne Claus
In this paper, we present a robust and efficient unfitted concurrent multiscale method for continuum-continuum coupling, based on the Cut Finite Element Method (CutFEM). The comput…
Concurrent multiscale analysis without meshing: Microscale representation with CutFEM and micro/macro model blending
Ehsan Mikaeili, Susanne Claus, Pierre Kerfriden
In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed…
Addressing materials' microstructure diversity using transfer learning
Aurèle Goetz, Ali Riza Durmaz, Martin Müller +4
Materials' microstructures are signatures of their alloying composition and processing history. Therefore, microstructures exist in a wide variety. As materials become increasingly…
A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features
Vasilis Krokos, Viet Bui Xuan, Stéphane P. A. Bordas +2
Multiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale…
On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning
I. B. C. M. Rocha, P. Kerfriden, F. P. van der Meer
Concurrent multiscale finite element analysis (FE2) is a powerful approach for high-fidelity modeling of materials for which a suitable macroscopic constitutive model is not availa…
A CutFEM method for two-phase flow problems
Susanne Claus, Pierre Kerfriden
In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalt…
Isogeometric analysis with local adaptivity based on a posterior error estimation for elastodynamics
Peng Yu, Cosmin Anitescu, Satyendra Tomar +2
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on…
A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems
Susanne Claus, Pierre Kerfriden
In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of t…
CAD model simplification error estimation for electrostatics problems
Navid Rahimi, Pierre Kerfriden, Frank C Langbein +1
Simplifying the geometry of a CAD model using defeaturing techniques enables more efficient discretisation and subsequent simulation for engineering analysis problems. Understandin…
Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method
Octavio Andrés González Estrada, Juan José Ródenas García, Stéphane Bordas +3
Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally imp…
Nitsche's method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling
Vinh Phu Nguyen, Pierre Kerfriden, Susanne Claus +1
A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming for…
Nitsche's method for two and three dimensional NURBS patch coupling
Vinh Phu Nguyen, Pierre Kerfriden, Marco Brino +2
A Nitche's method is presented to couple non-conforming two and three dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We p…
A goal-oriented reduced basis method for the wave equation in inverse analysis
Khac Chi Hoang, Pierre Kerfriden, Stephane P. A. Bordas
In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine parameter dependence. The essential new ingredie…
Isogeometric cohesive elements for two and three dimensional composite delamination analysis
Vinh Phu Nguyen, Pierre Kerfriden, Stephane Bordas
Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non…
Space-time goal-oriented reduced basis approximation for linear wave equation
Khac Chi Hoang, Pierre Kerfriden, Stephane P. A. Bordas
In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by…
Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress
Olivier Allix, Pierre Gosselet, Pierre Kerfriden +1
This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composit…
Certification of projection-based reduced order modelling in computational homogenisation by the Constitutive Relation Error
Pierre Kerfriden, Juan José Ródenas García, Stéphane Pierre-Alain Bordas
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound re…
Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
Octavio Andrés González Estrada, E. Nadal, J. J. Ródenas +3
During the last decade there has been an increase on the use of goal-oriented error estimates which help to quantify and control the local error on a quantity of interest (QoI) tha…
A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics
Pierre Kerfriden, Olivier Goury, Timon Rabczuk +1
We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition…
Statistical extraction of process zones and representative subspaces in fracture of random composite
Pierre Kerfriden, Karl Michael Schmidt, Timon Rabczuk +1
We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process c…
On the role of enrichment and statical admissibility of recovered fields in a-posteriori error estimation for enriched finite element methods
Octavio A. González-Estrada, Juan José Ródenas, Stéphane P. A. Bordas +3
Purpose: This paper aims at assessing the effect of (1) the statical admissibility of the recovered solution; (2) the ability of the recovered solution to represent the singular so…
Improved multiscale computational strategies for delamination
Olivier Allix, Pierre Gosselet, Pierre Kerfriden
This paper presents a three-scale computational strategy for the study of composite modeled at the mesoscale so that delamination can be reliably simulated. The solver is based on…