A k‐means clustering machine learning‐based multiscale method for anelastic heterogeneous structures with internal variables
A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss poin...
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| Published in | International journal for numerical methods in engineering Vol. 123; no. 9; pp. 2012 - 2041 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
15.05.2022
Wiley Subscription Services, Inc Wiley |
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| Online Access | Get full text |
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| Abstract | A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k‐means clustering—machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE2 calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi‐brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions. |
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| AbstractList | A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k‐means clustering—machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE2 calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi‐brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions. A new machine-learning based multiscale method, called k-means FE 2 , is introduced to solve general nonlinear multiscale problems with internal variables and loading history-dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k-means clustering-machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE 2 calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi-brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions. A new machine‐learning based multiscale method, called k‐means FE, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k‐means clustering—machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi‐brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions. |
| Author | He, Qi‐Chang Yvonnet, Julien Benaimeche, Mohamed Amine Bary, Benoit |
| Author_xml | – sequence: 1 givenname: Mohamed Amine surname: Benaimeche fullname: Benaimeche, Mohamed Amine organization: MSME, CNRS UMR 8208 – sequence: 2 givenname: Julien surname: Yvonnet fullname: Yvonnet, Julien email: julien.yvonnet@univ-eiffel.fr organization: MSME, CNRS UMR 8208 – sequence: 3 givenname: Benoit surname: Bary fullname: Bary, Benoit organization: Université Paris‐Saclay, CEA, Service d'Étude du Comportement des Radionucléides – sequence: 4 givenname: Qi‐Chang surname: He fullname: He, Qi‐Chang organization: MSME, CNRS UMR 8208 |
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| Keywords | Homogenization FE2 k-means clustering Nonlinear Multiscale Machine learning |
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| Snippet | A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and... A new machine‐learning based multiscale method, called k‐means FE, is introduced to solve general nonlinear multiscale problems with internal variables and... A new machine-learning based multiscale method, called k-means FE 2 , is introduced to solve general nonlinear multiscale problems with internal variables and... |
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| StartPage | 2012 |
| SubjectTerms | Anelasticity Clustering Dependent variables Elastoplasticity Engineering Sciences FE2 Finite element method homogenization k‐means clustering Load history Machine learning Mechanical properties multiscale Multiscale analysis nonlinear Radioactive wastes |
| Title | A k‐means clustering machine learning‐based multiscale method for anelastic heterogeneous structures with internal variables |
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