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Correction published on 6 November 2019, see Math. Comput. Appl. 2019, 24(4), 95.
Open AccessFeature PaperArticle

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

Efficient Methods for Mechanical Analysis, Institute of Applied Mechanics (CE), University of Stuttgart, 70569 Stuttgart, Germany
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Math. Comput. Appl. 2019, 24(2), 56; https://doi.org/10.3390/mca24020056
Received: 31 March 2019 / Revised: 24 May 2019 / Accepted: 24 May 2019 / Published: 27 May 2019
The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5–100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method. View Full-Text
Keywords: computational homogenization; large strain; finite deformation; geometric nonlinearity; reduced basis; reduced-order model; sampling; Hencky strain computational homogenization; large strain; finite deformation; geometric nonlinearity; reduced basis; reduced-order model; sampling; Hencky strain
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Kunc, O.; Fritzen, F. Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling. Math. Comput. Appl. 2019, 24, 56.

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