A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations

Casenave, Fabien; Akkari, Nissrine; Bordeu, Felipe; Rey, Christian; Ryckelynck, David

doi:10.1002/nme.6187

Cited by 27 publications

(37 citation statements)

References 46 publications

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“…We consider the model introduced in [12], which we briefly recall below for the sake of completeness. The structure of interest is noted Ω and its boundary ∂Ω, where ∂Ω = ∂Ω D ∪ ∂Ω N such that ∂Ω D ∩ ∂Ω N = ∅, see Figure 2.…”

Section: High-fidelity Elastoviscoplastic Modelmentioning

confidence: 99%

“…For instance, the integrals in (6) and (7) are computed in computational complexity dependent on N in the general case. We briefly present the choices made in our previous work [12]: the offline stage is composed of the following steps • data generation: this corresponds to the generation of the numerical approximation of the solutions to (1a)-(1f), using the Newton algorithm (2). Multiple temporal solutions can be considered, for different loading conditions.…”

Section: Reduced Order Modelingmentioning

confidence: 99%

“…We now briefly present how this reduced quadrature formula is obtained and we refer to [12,23] for more details. We denote h q := σ (u µ (q//n)+1 ), y : ψ (q%n)+1 ∈ L 2 (Ω), where // and % are respectively the quotient and the remainder of the Euclidean division, Z is a subset of [1; N G ] of size d, with N G the number of integration points, and J Z ∈ R nNc×d and g ∈ N nNc are such that for all 1 ≤ q ≤ nN c and all 1 ≤ k ≤ d,…”

Section: Reduced Order Modelingmentioning

confidence: 99%

“…Input: tolerance Gappy−POD , cumulated plasticity snapshots set {p µi } 1≤i≤Nc , indices of the integration points of the reduced quadrature formula Output: indices for online material law computation, ROM-Gappy-POD matrix 1 Apply the snapshot POD (Algorithm 1) on the high-fidelity snapshots {p µi } 1≤i≤Nc to obtain the vectors ψ p i , 1 ≤ i ≤ n p , orthonormal with respect to the L 2 (Ω)-inner product 2 Apply the EIM to the collection of vectors ψ p i , 1 ≤ i ≤ n p , to select n p distinct indices and complete (without repeat) this set of indices by the indices of the integration points of the reduced quadrature formula Input: online variability µ, indices for online material law computation, ROM-Gappy-POD matrix Output: reconstructed value for p on the complete domain Ω The ROM-Gappy-POD reconstruction is well-posed, since the linear system considered in the online stage of Algorithm 4 is invertible, see [12,Proposition 1].…”

Section: Reduced Order Modelingmentioning

confidence: 99%

“…[O2] the ROM-Gappy-POD residual (13) is highly correlated to the error (12), so that the proposed error indicator (19) can be used in the online stage as described in the workflow illustrated in Figure 4 to correct online variabilities of the temperature loading not encountered during the offline stage.…”

Section: High-pressure Turbine Bladementioning

confidence: 99%

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An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Casenave

Akkari

2019

MCA

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The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes the classical unenriched proper orthogonal decomposition method fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the error indicator becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.Computing lifetime predictions for high-pressure turbine blades is a challenging task: meshes involve large numbers of degrees of freedom to account for local structures such as the internal cooling channels, the behavior laws are strongly nonlinear with many internal variables, and a large number of cycles has to be computed. Besides, the temperature loading is poorly known in the outlet section of the combustion chamber. Our team has proposed in [12] a nonintrusive reduced order model (ROM) strategy in parallel computation with distributed memory to mitigate the runtime issues: a domain decomposition method is used to compute the first cycle, and the reduced order model is used to speed up the computation of the following cycles, which can be considered as a reduced order model-based temporal extrapolation. As pointed out in [12], errors are accumulated during this temporal extrapolation. Moreover, quantifying the uncertainty on the lifetime with respect to some statistical description of the temperature loading using an already constructed reduced order model would introduce additional errors. In this context, error indicator-based enrichment of reduced order models is the topic of the present work.Error estimation for reduced model predictions is a topic that receives interest in the scientific literature. The reduced basis method [32,28] for parametrized problems is a reduced order modeling method that intrinsically relies on efficient a posteriori error bounds of the error between the reduced prediction and the reference high-fidelity (HF) solution. This method consists in a greedy enrichment of a current reduced order basis by the high-fidelity solution at the parametric...

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Section: High-fidelity Elastoviscoplastic Modelmentioning

confidence: 99%

Section: Reduced Order Modelingmentioning

confidence: 99%

Section: Reduced Order Modelingmentioning

confidence: 99%

Section: Reduced Order Modelingmentioning

confidence: 99%

Section: High-pressure Turbine Bladementioning

confidence: 99%

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An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Casenave

Akkari

2019

MCA

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An adaptive projection‐based model reduction method for nonlinear mechanics with internal variables: Application to thermo‐hydro‐mechanical systems

Iollo

Sambataro

Taddei

2022

Numerical Meth Engineering

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We propose a projection‐based monolithic model order reduction procedure for a class of problems in nonlinear mechanics with internal variables. The work is motivated by applications to thermo‐hydro‐mechanical (THM) systems for radioactive waste disposal. THM equations model the behavior of temperature, pore water pressure, and solid displacement in the neighborhood of geological repositories, which contain radioactive waste and are responsible for a significant thermal flux toward the Earth's surface. We develop an adaptive sampling strategy based on the POD‐Greedy method, and we develop an element‐wise empirical quadrature hyper‐reduction procedure to reduce assembling costs. We present numerical results for a two‐dimensional THM system to illustrate and validate the proposed methodology.

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A projection‐based reduced‐order model for parametric quasi‐static nonlinear mechanics using an open‐source industrial code

Agouzal,

Argaud,

Bergmann

et al. 2023

Numerical Meth Engineering

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We propose a projection‐based model order reduction procedure for a general class of parametric quasi‐static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code codeaster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high‐fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD‐Greedy strategy, and we develop an hyper‐reduction strategy based on an element‐wise empirical quadrature in order to speed up the assembly costs of the reduced‐order model by building an appropriate reduced mesh. We introduce a cost‐efficient error indicator which relies on the reconstruction of the stress field by a Gappy‐POD strategy. We present numerical results for a three‐dimensional elastoplastic system in order to illustrate and validate the methodology.

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A nonintrusive distributed reduced‐order modeling framework for nonlinear structural mechanics—Application to elastoviscoplastic computations

Cited by 27 publications

References 46 publications

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

An adaptive projection‐based model reduction method for nonlinear mechanics with internal variables: Application to thermo‐hydro‐mechanical systems

A projection‐based reduced‐order model for parametric quasi‐static nonlinear mechanics using an open‐source industrial code

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