A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling
A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear s...
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| Published in: | International journal for numerical methods in engineering Vol. 123; no. 12; pp. 2738 - 2759 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Hoboken, USA
John Wiley & Sons, Inc
30.06.2022
Wiley Subscription Services, Inc |
| Subjects: | |
| ISSN: | 0029-5981, 1097-0207 |
| Online Access: | Get full text |
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| Abstract | A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear strain–stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure‐preserving approach for constructing a data‐driven model featuring both the form‐agnostic advantage of purely phenomenological data‐driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi‐scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi‐scale, fluid‐structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric. |
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| AbstractList | A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear strain–stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure‐preserving approach for constructing a data‐driven model featuring both the form‐agnostic advantage of purely phenomenological data‐driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi‐scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi‐scale, fluid‐structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric. |
| Author | Farhat, Charbel Avery, Philip As'ad, Faisal |
| Author_xml | – sequence: 1 givenname: Faisal orcidid: 0000-0002-8538-9283 surname: As'ad fullname: As'ad, Faisal email: faisal3@stanford.edu organization: Stanford University – sequence: 2 givenname: Philip orcidid: 0000-0002-1310-6790 surname: Avery fullname: Avery, Philip organization: Stanford University – sequence: 3 givenname: Charbel orcidid: 0000-0003-2563-8820 surname: Farhat fullname: Farhat, Charbel organization: Stanford University |
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| SubjectTerms | artificial neural network Artificial neural networks Computer architecture Computer simulation constitutive modeling convexity Dynamic stability Finite element method hyperelasticity Learning machine learning Mechanics Neural networks Noise sensitivity Parachute canopies Regression models Rigid structures Robustness (mathematics) Solid mechanics stability Strain supersonic parachute inflation dynamics Training Woven fabrics |
| Title | A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling |
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