Stéphane Pierre Alain Bordas

Stéphane Pierre Alain Bordas
University of Luxembourg · Institute of computational engineering

PhD, MSc, MEng, BSc

About

382
Publications
178,273
Reads
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16,252
Citations
Introduction
Computational mechanics researcher - moving boundary problems, advanced discretisation techniques, surgical simulation, fracture mechanics, isogeometric analysis, extended finite element method, open source computational mechanics codes, MATLAB, C++
Additional affiliations
November 2013 - present
University of Luxembourg
Position
  • Professor of Computational Mechanics
September 2013 - December 2025
University of Luxembourg
Position
  • Head of Department
January 2012 - January 2017
Cardiff University
Position
  • ERC Starting Independent Research
Description
  • real time simulation; cutting; heterogeneous materials; surgical simulation;

Publications

Publications (382)
Preprint
Full-text available
There has been a growing interest for controlled heat flux manipulation to increase the efficiency of thermal apparatus. Heat manipulators control and manipulate heat flow. A key to the effective performance of these heat manipulators is their thermal design. Such designs can be achieved by a periodic assembly of unit cells (known as metamaterials...
Article
The paper presents a novel approach for multi-frequency acoustic topology optimization of sound-absorption materials. In this work, the isogeometric boundary element method based on subdivision surfaces is used to solve Helmholtz equations defined in infinite domains. To avoid time-consuming frequency sweep, we adopt series expansion method to deco...
Article
Isogeometric Analysis (IGA) provides an alternative to Lagrange based finite element methods by representing the geometry and field with the same Non-Uniform Rational B-Splines (NURBS) shape functions within a weak Galerkin formulation. IGA has proven to be highly efficient in solving the Helmholtz equation, due to the ease with which the order and...
Article
This paper presents a non-intrusive scaled boundary finite element method to consider multiple input uncertainties, viz., material and geometry. The types of geometric uncer- tainties considered include the shape and size of inclusions. The inclusions are implicitly defined, and a robust framework is presented to treat the interfaces, which does no...
Article
A recovery-based error indicator developed to evaluate the quality of polygonal finite element approximations is presented in this paper. Generalizations of the finite element method to arbitrary polygonal meshes have been increasingly investigated in the last years, as they provide flexibility in meshing and improve solution accuracy. As any numer...
Preprint
Full-text available
We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is designed to be executed by the modular robot itself and is based on an distributed iterative solution of mechanical equilib...
Article
Full-text available
We present a distributed framework for predicting whether a planned reconfiguration step of a modular robot will mechanically overload the structure, causing it to break or lose stability under its own weight. The algorithm is executed by the modular robot itself and based on a distributed iterative solution of mechanical equilibrium equations deri...
Article
Full-text available
The majority of topology optimization methods for porous infill designs is based on the assumption of deterministic loads. However, in practice, quantities such as positions, weights, and directions of applied loads may change accidentally. Deterministic load-based designs might deliver poor structural performance under loading uncertainties. Such...
Article
In this paper, system identification is coupled with optimization-based damage detection to provide accurate localization of cracks in thin plates, under dynamic loading. Detection relies on exploitation of strain measurements from a network of sensors deployed onto the plate structure. The data-driven approach is based on the detection of discrepa...
Preprint
Full-text available
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank-Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, t...
Poster
Full-text available
In this poster, we present our new hierarchical a posteriori error estimation method for the spectral fractional Laplacian equation with homogeneous Dirichlet boundary condition. The numerical results show the adaptively refined mesh we obtain using our method as well as a convergence comparison where we can notice the sharpness of the estimator an...
Article
Full-text available
The paper aims to evaluate the performance of the Lagrange-based Finite Element Method and the Non Uniform Rational B-Splines Isogeometric Analysis of time-harmonic acoustic exterior scattering problems using high-order local absorbing boundary conditions, in particular based on the Karp's and Wilcox's farfield expansions. The analysis of accuracy...
Chapter
Full-text available
The COVID-19 pandemic has been a significant concern worldwide. The pandemic has demonstrated that public health issues are not merely a health concern, but also affect society as a whole. In this chapter, we address the importance of bringing together the world's scientists to find appropriate solutions for controlling and managing the COVID-19 pa...
Article
The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse‐grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria – that drive refining coarse‐grained regions and/or increasing fully‐resolve...
Article
Full-text available
This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severe...
Preprint
Full-text available
Finite Element Analysis (FEA) for stress prediction in structures with microstructural features is computationally expensive since those features are much smaller than the other geometric features of the structure. The accurate prediction of the additional stress generated by such microstructural features therefore requires a very fine FE mesh. Omi...
Article
Full-text available
Isogeometric boundary element method is a computer simulation algorithm that can directly utilize the data of a geometric model represented by its surface. Catmull-Clark subdivision surfaces are a widely used technique in 3D computer graphics to construct complicated geometries. In the present work, we combine Catmull-Clark subdivision surfaces wit...
Conference Paper
Full-text available
Large-scale 3D autonomous self-reconfigurable modular robots are made of numerous interconnected robotic modules that operate in a close packing. The modules are assumed to have their own CPU and memory, and are only able to communicate with their direct neighbors. As such, the robots embody a special computing architecture: a distributed memory an...
Preprint
Full-text available
Spheroids encapsulated within alginate capsules are emerging as suitable in vitro tools to investigate the impact of mechanical forces on tumor growth since the internal tumor pressure can be retrieved from the deformation of the capsule. Here we focus in particular on the Cellular Capsule Technology (CCT). We show that a modeling approach accounti...
Article
This paper presents an n-th high order perturbation-based stochastic isogeometric Kirchhoff–Love shell method, formulation and implementation for modeling and quantifying geometric (thickness) uncertainty in thin shell structures. Firstly, the Non-Uniform Rational B-Splines (NURBS) is used to describe the geometry and interpolate the variables in a...
Preprint
Full-text available
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future bench...
Article
Full-text available
In this paper, we establish a coupled damage-plastic constitutive model in the scheme of small deformation assumption, based on a continuum damage mechanics model proposed by Lemaitre, for the thin-walled circular steel tubes widely used in space structures. First, a new damage evolution law is developed for steel tubes. Then the isotropic damage-p...
Article
Full-text available
The aim of this work is to characterize the mechanical parameters governing the in-plane behavior of human skin and, in particular, of a keloid-scar. We consider 2D hyperelastic bi-material model of a keloid and the surrounding healthy skin. The problem of finding the optimal model parameters that minimize the misfit between the model observations...
Article
We propose a generalized quasicontinuum method to model the mechanical response of 3D lattice structures. The method relies on the spatial coupling of fully-resolved domains and coarse-grained domains. In the fully-resolved domain, the full micro-structure is taken into account. In the coarse-grained domain, the kinematics of the micro-structure ar...
Article
Full-text available
The aim of this paper is that the precise description of damage behavior is crucial to well catch the mechanical behavior of structures in the dynamic numerical simulation, and address the issue on the coupled plastic-damage constitutive model for circular steel tubes of reticulated shells under severe earthquake. Continuum Damage Mechanics (CDM) c...
Conference Paper
Full-text available
The search space for new thermoelectric oxides has been limited to the alloys of a few known systems, such as ZnO, SrTiO3 and CaMnO3. Notwithstanding the high power factor, their high thermal conductivity is a roadblock in achieving higher efficiency. In this paper, we apply machine-learning models for discovering novel transition metal oxides with...
Article
Full-text available
A parametrized reduced order modeling methodology for cracked two dimensional solids is presented, where the parameters correspond to geometric properties of the crack, such as location and size. The method follows the offline‐online paradigm, where in the offline, training phase, solutions are obtained for a set of parameter values, corresponding...
Article
In this paper, we extend the concept of MINI element over triangles to star convex arbitrary polytopes. This is achieved by employing the volume averaged nodal projection (VANP) method over polytopes in combination with the strain smoothing technique. Within this framework, the dilatation strain is projected onto the linear approximation space, thu...
Article
Full-text available
We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis fun...
Preprint
Full-text available
In this paper, the performance of the finite element method based on Lagrange basis functions and the Non Uniform Rational B-Splines (NURBS) based Iso-Geometric Analysis (IGA) are systematically studied for solving time-harmonic acoustic scattering problems. To assess their performance, the numerical examples are presented with truncated absorbing...
Article
Full-text available
Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. In the latter case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separatio...
Article
This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spl...
Preprint
Full-text available
Writing a good scientific paper is not easy for many graduate students. To help these students, particularly those working on the field of computational engineering and sciences, this paper presents some writing guidelines that we have collected and used for the last twenty years. The guidelines consist of three major parts. The first part is a wri...
Article
Full-text available
This paper surveys both the clinical applications and main technical innovations related to steered needles, with an emphasis on neurosurgery. Technical innovations generally center on curvilinear robots that can adopt a complex path that circumvents critical structures and eloquent brain tissue. These advances include several needle-steering appro...
Article
Full-text available
We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation is general and allows the f...
Article
Full-text available
Thrombosis plays a crucial role in atherosclerosis or in haemostasis when a blood vessel is injured. This article focuses on using a meshless particle-based Lagrangian numerical technique, the smoothed particles hydrodynamic (SPH) method, to study the flow behaviour of blood and to explore the flow parameters that induce formation of a thrombus in...
Article
Full-text available
We study the application of a B-splines Finite Element Method to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing Boundary Conditions (ABCs) are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance...
Conference Paper
Full-text available
A particularly challenging issues in manufacturing of medical gas valves and regulators, are gas-dynamic pressure surges and adiabatic compression phenomena, along with the design and optimisation of the complex geometries of valves. Depending on the field of application, the pressure surges can lead to considerable malfunctions, and in very critic...
Article
Full-text available
Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, a major constraint in structural designs. Computational modelling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights...
Article
The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials...
Article
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future bench...
Article
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed...
Article
Full-text available
Errors in biomechanics simulations arise from modelling and discretization. Modelling errors are due to the choice of the mathematical model whilst discretization errors measure the impact of the choice of the numerical method on the accuracy of the approximated solution to this specific mathematical model. A major source of discretization errors i...
Article
Le travail proposé concerne la prédiction de la réponse numérique d'une structure biomécanique sou-mise à un état de chargement externe inconnu. La méthodologie s'appuie sur la modélisation de structures homogènes puis hétérogènes, telles que des tissus cutanés sains ou pathologiques accessibles expé-rimentalement et soumis à des conditions aux lim...
Article
Full-text available
La peau humaine se comporte comme une membrane élastique précontrainte. La présence de sites anatomiques favorables à l'apparition de certaines tumeurs, une chéloïde dans notre cas, alors que d'autres en sont systématiquement dépourvus atteste de l'importance de l'environnement mécanique du tissu. Par conséquent, une caractérisation de la peau avec...
Article
Full-text available
In this study, a gradient weighted extended finite element method (GW-XFEM) is presented for the analysis of fracture problems. For this method, the domain discretization is the same as the standard XFEM. However, the gradient field is constructed by considering the influences of the element itself and its adjacent elements. Based on the Shepard in...
Article
A computational approach that couples molecular-dynamics (MD) and the-finite-element-method (FEM) technique is here proposed for the theoretical study of the dynamics of particles subjected to electromechanical forces. The system consists of spherical particles (modeled as micrometric rigid bodies with proper densities and dielectric functions) sus...
Article
Full-text available
We present numerical computation of stresses under fretting fatigue conditions derived from closed form expressions. The Navier-Cauchy equations, that govern the problem, are solved with strong and weak form meshless numerical methods. The results are compared to the solution obtained from well-established commercial package ABAQUS, which is based...
Preprint
A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed...
Article
Full-text available
The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requir...
Research
In this paper, the performance of the finite element method based on Lagrange basis functions and the Non Uniform Rational B-Splines (NURBS) based iso-geometric analysis (IGA) are systematically studied in solving the exterior acoustic problems. To assess the performance, three numerical examples are presented with a truncated boundary. In the firs...
Article
Full-text available
In this paper, the cell based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo\'eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of s...