Nitsche’s method for two and three dimensional NURBS patch coupling

in Computational Mechanics (in press)

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear ... [more ▼]

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications. [less ▲]

An equation-free, nested, concurrent multiscale approach without scale-separation

Scientific Conference (2018, September)

Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation

in Computer Methods in Applied Mechanics and Engineering (2018), 342

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 the recently developed ... [more ▼]

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 the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalization of the Iso-Geometric Analysis (IGA).Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing Polynomial splines over Hierarchical T-meshes (PHT)-splines to represent the solution field. The proposed strategy of local adaptivity, wherein a posteriori error estimators are computed based on inexpensive hierarchical h-refinement, aims to control the discretization error within a frequency band. The approach sweeps from lower to higher frequencies, refining the mesh appropriately so that each of the free vibration mode within the targeted frequency band is sufficiently resolved. Through several numerical examples, we show that the GIFT framework is a powerful and versatile tool to perform local adaptivity in structural dynamics. We also show that the proposed adaptive local h-refinement scheme allows us to achieve significantly faster convergence rates than a uniform h-refinement. [less ▲]

An equation-free multiscale method applied to discrete networks

Scientific Conference (2017, June 06)

Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales

in International Journal for Numerical Methods in Engineering (2017), 110(2), 103132

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion ... [more ▼]

This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. We typically consider linear elliptic diffusion problems in randomly packed particulate composites. Our work extends the pioneering work presented in [26,32] in order to bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic, and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager-Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss-Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation. [less ▲]

Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

in International Journal of Fracture (2016)

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

in Computer Methods in Applied Mechanics and Engineering (2016)

Error estimation and space-time adaptivity for the isogeometric analysis of transient structural dynamics

Scientific Conference (2016, April 01)

This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local ... [more ▼]

This paper presents a new adaptive scheme for the error-controlled simulation of transient dynamics problem. We rely on spline bases for the higher-order spatial description of our kinematic fields. Local adaptivity is performed by employing a hierarchical T-mesh technology, in combination with geometry independent field approximation. The Newmark algorithm is chosen to solve the semidiscrete equation of motion. We will present some simple local error estimates to drive the adaptivity, and show how we can ensure that the mechanical energy of conservative systems is preserved during the refinement process. [less ▲]

Isogeometric boundary element methods for linear elastic fracture mechanics

Report (2016)

Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety

Scientific Conference (2015, November 18)

Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel  Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety ... [more ▼]

Authors: S. P. A. Bordas, L. A. A. Beex, P. Kerfriden, D. A. Paladim, O. Goury, A. Akbari, H. Rappel  Multi-scale methods for fracture: model learning across scales, digital twinning and factors of safety Fracture and material instabilities originate at spatial scales much smaller than that of the structure of interest: delamination, debonding, fibre breakage, cell-wall buckling, are examples of nano/micro or meso-scale mechanisms which can lead to global failure of the material and structure. Such mechanisms cannot, for computational and practical reasons, be accounted at structural scale, so that acceleration methods are necessary.  We review in this presentation recently proposed approaches to reduce the computational expense associated with multi-scale modelling of fracture. In light of two particular examples, we show connections between algebraic reduction (model order reduction and quasi-continuum methods) and homogenisation-based reduction. We open the discussion towards suitable approaches for machine-learning and Bayesian statistical based multi-scale model selection. Such approaches could fuel a digital-twin concept enabling models to learn from real-time data acquired during the life of the structure, accounting for “real” environmental conditions during predictions, and, eventually, moving beyond the “factors of safety” era. [less ▲]