Work

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

Year: 2019

Type: article

Abstract: 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.

Source: Mathematical and Computational Applications

DOI: 10.3390/mca24020056

Authors: Oliver Kunc, Felix Fritzen

Institution: University of Stuttgart

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,013

Funder: Deutsche Forschungsgemeinschaft