G-MAP123: A mechanistic-based data-driven approach for 3D nonlinear elastic modeling — Via both uniaxial and equibiaxial tension experimental data

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Mechanical Engineering Department

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Jie Chen, Hang Yang, Khalil I. Elkhodary, Shan Tang, Xu Guo

Document Type

Research Article

Publication Title

Extreme Mechanics Letters

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This work proposes a data-driven approach, G-MAP123, using discrete data directly for nonlinear elastic materials to solve boundary value problems, avoiding analytic-function based constitutive models. G-MAP123 is formulated in the current configuration in which the Cauchy stress and the left Cauchy–Green strain are adopted as the stress–strain measures of the data. Data generated under both uniaxial tension and equibiaxial tension experiments is used. A data search employing stress triaxiality as the index is here proposed for the stress update. Furthermore, including additional data from other loading paths is also rendered possible. Comparison with reference analytic-function based models such as Arruda–Boyce, Yeoh, Mooney–Rivlin and Van der Waals is carried out. Results show that the predictions from G-MAP123 are in agreement with all those of the reference models. Moreover, the classic experimental data of rubber from Treloar is here used to demonstrate the capability of the proposed G-MAP123 in the practical setting. This approach opens a new avenue to modeling soft materials accurately and conveniently at large deformation, directly from the data.

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