Model order reduction for hyperelastic materials

Niroomandi, Siamak; Alfaro, Icíar; Cueto, Elías; Chinesta, Francisco

doi:10.1002/nme.2733

Cited by 64 publications

(60 citation statements)

References 17 publications

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“…It is now clear that the use of model reduction seems to be an appealing alternative for reaching such performances. However, techniques based on the use of POD, POD with interpolation (PODI), even combined with asymptotic numerical methods to avoid the computation of the tangent stiffness matrix [28,54], exhibit serious difficulties to fulfil such requirements as discussed in [60][61][62][63].…”

Section: Surgery Simulatorsmentioning

confidence: 99%

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Chinesta

Leygue²,

Bordeu³

et al. 2013

Arch Computat Methods Eng

280

291

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to highdimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with highdimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

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Section: Surgery Simulatorsmentioning

confidence: 99%

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

Chinesta

Leygue²,

Bordeu³

et al. 2013

Arch Computat Methods Eng

280

291

View full text Add to dashboard Cite

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“…There is an extensive literature regarding this issue. The interested readers can refer to [1][2][3][4][5][6][7][8][9][10][11][12] and the numerous references therein. The extraction of the reduced basis is the key point when using POD-based model order reduction, as well as its adaptivity when addressing scenarios far from the ones considered in the construction of the reduced basis [13,14].…”

Section: Introductionmentioning

confidence: 99%

On the space-time separated representation of integral linear viscoelastic models

Ammar¹,

Zghal²,

Morel³

et al. 2015

Comptes Rendus. Mécanique

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. The analysis of materials mechanical behavior involves many computational challenges. In this work, we are addressing the transient simulation of the mechanical behavior when the time of interest is much larger than the characteristic time of the mechanical response. This situation is encountered in many applications, as for example in the simulation of materials aging, or in structural analysis when small-amplitude oscillatory loads are applied during a long period, as it occurs for example when characterizing viscoelastic behaviors by calculating the complex modulus or when addressing fatigue simulations. Moreover, in the case of viscoelastic behaviors, the constitutive equation is many times expressed in an integral form avoiding the necessity of using internal variables, fact that results in an integro-differential model. In order to efficiently simulate such a model, we explore in this work the use of a space-time separated representation.© 2015 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.r é s u m é L'analyse du comportement mécanique des matériaux entraîne de nombreuses difficultés du point de vue numérique. Dans ce travail, nous allons nous focaliser sur l'une d'entre elles, celle associée à la simulation transitoire du comportement mécanique quand l'intervalle temporel d'intérêt est substantiellement plus long que le temps caractéristique associé à la réponse mécanique. Cette situation est fréquemment retrouvée dans la caractérisation rhéologique des matériaux viscoélastiques (pour la détermination du module complexe) ainsi que quand on s'attaque à la simulation de la fatigue. De plus, dans le cas des matriaux viscoélastiques, le comportement est généralement décrit par une loi de comportement intégrale qui évite le besoin d'utiliser des variables internes, donnant lieu * Corresponding author.

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“…In particular, projection-based (a posteriori) model order reduction techniques very often lack of efficiency in non-linear problems, where the complete system of equations needs to be rebuilt in order to perform consistent linearization, thus loosing all the pretended gain. Methods as the empirical interpolation method [13] or the coupling with Asymptotic Numerical Methods [14] aim at solving these deficiencies.…”

Section: Introductionmentioning

confidence: 99%

Towards a pancreatic surgery simulator based on model order reduction

Mena

Bel

Alfaro

et al. 2015

Adv. Model. and Simul. in Eng. Sci.

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In this work a pancreatic surgery simulator is developed that provides the user with haptic feedback. The simulator is based on the use of model order reduction techniques, particularly Proper Generalized Decomposition methods. The just developed simulator presents some notable advancements with respect to existing works in the literature, such as the consideration of non-linear hyperelasticity for the constitutive modeling of soft tissues, an accurate description of contact between organs and momentum and energy conserving time integration schemes. Pancreas, liver, gall bladder, and duodenum are modeled in the simulator, thus providing with a very realistic and immersive perception to the user.

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Model order reduction for hyperelastic materials

Cited by 64 publications

References 17 publications

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

On the space-time separated representation of integral linear viscoelastic models

Towards a pancreatic surgery simulator based on model order reduction

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