Reduced order modeling strategies for computational multiscale fracture

Oliver, J.; Caicedo, M.; Huespe, Alfredo Edmundo; Hernández, J.A.; Roubin, Emmanuel

doi:10.1016/j.cma.2016.09.039

Cited by 95 publications

(67 citation statements)

References 22 publications

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“…The ROM is expected to play a major role in facilitating real-time turnaround of computational results. It has been applied into a number of fields, for example, nonlinear large-scale systems, 13 ocean modelling, 14,15 sensor location optimisation, 16 air pollution modelling, 17 shape optimisation, 18 porous media problems, 19 aerospace, 20,21 optimal control, 22,23 multiscale fracture, 24 shallow water, [25][26][27] and neutron problems. 28 Reduced order models can be broadly divided into 2 types: intrusive ROMs and non-intrusive ROMs (NIROMs).…”

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confidence: 99%

Model identification of reduced order fluid dynamics systems using deep learning

Wang

Xiao

Fang

et al. 2017

Numerical Methods in Fluids

197

114

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SUMMARYThis paper presents a novel model reduction method: Deep Learning Reduced Order Model (DLROM), which is based on proper orthogonal decomposition (POD) and deep learning methods. The deep learning approach is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the non-linear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The Long Short-Term Memory network (LSTM) is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system. The reduced order model (ROM) based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new ROM is evaluated using two numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.

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mentioning

confidence: 99%

Model identification of reduced order fluid dynamics systems using deep learning

Wang

Xiao

Fang

et al. 2017

Numerical Methods in Fluids

197

114

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“…Multiple approaches can be used to reduce the computational effort, including reducedorder modelling at the level of each RVE or considering equivalent surrogate models, see e.g. [28,20,25]. In this contribution, we focus on a yet another approach to reduce the computational effort in the context of the micromorphic computational homogenization [22] by decreasing the number of macroscopic integration points.…”

Section: Introductionmentioning

confidence: 99%

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Rokoš

Zeman

Doškář

et al. 2020

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

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Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a transformation, effective properties of a metamaterial may change significantly. To capture this phenomenon accurately and efficiently, homogenization schemes are required that reflect microstructural as well as macro-structural instabilities, large deformations, and non-local effects. To this end, a micromorphic computational homogenization scheme has recently been developed, which employs the particular microstructural transformation as a non-local mechanism, magnitude of which is governed by an additional coupled partial differential equation. Upon discretizing the resulting problem it turns out that the macroscopic stiffness matrix requires integration of macro-element basis functions as well as their derivatives, thus calling for a higher-order integration rules. Because evaluation of constitutive law in multiscale schemes involves an expensive solution of a non-linear boundary value problem, computational efficiency can be improved by reducing the number of integration points. Therefore, the goal of this paper is to investigate reduced-order schemes in computational homogenization, with emphasis on the stability of the resulting elements. In particular, arguments for lowering the order of integration from the expensive mass-matrix to a cheaper stiffness-matrix equivalent are first outlined. An efficient one-point integration quadrilateral element is then introduced and proper hourglass stabilization discussed. Performance of the resulting set of elements is finally tested on a benchmark bending example, showing that we achieve accuracy comparable to the full quadrature rules, whereas computational costs decrease proportionally to the reduction in the number of quadrature points used.

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“…Model order reduction (MOR) is a field considerably developed in computational simulations in engineering; such field has relevant applications in many other fields, like dynamics as explained in related works, 1-4 multiscale analysis, [5][6][7][8] and fluids analysis. [9][10][11] Related to the development of the MOR itself, several MOR with offline analysis are described in other works, 9,[12][13][14] or in online analysis as developed in previous works 1,2,10,15,16 ; several of them achieving meaningful results related to the processing time.…”

Section: Introductionmentioning

confidence: 99%

Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method

Nigro

Simões²,

Pimenta

et al. 2019

Numerical Meth Engineering

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Summary It is not new that model order reduction (MOR) methods are employed in almost all fields of engineering to reduce the processing time of complex computational simulations. At the same time, interior point methods (IPMs), a method to deal with inequality constraint problems (which is little explored in engineering), can be applied in many fields such as plasticity theory, contact mechanics, micromechanics, and topology optimization. In this work, a MOR based in Galerkin projection is coupled with the infeasible primal‐dual IPM. Such research concentrates on how to develop a Galerkin projection in one field with the interior point method; the combination of both methods, coupled with Schur complement, permits to solve this MOR similar to problems without constraints, leading to new approaches to adaptive strategies. Moreover, this research develops an analysis of error from the Galerkin projection related to the primal and dual variables. Finally, this work also suggests an adaptive strategy to alternate the Galerkin projection operator, between primal and dual variable, according to the error during the processing of a problem.

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Reduced order modeling strategies for computational multiscale fracture

Cited by 95 publications

References 22 publications

Model identification of reduced order fluid dynamics systems using deep learning

Model identification of reduced order fluid dynamics systems using deep learning

Reduced integration schemes in micromorphic computational homogenization of elastomeric mechanical metamaterials

Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method

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