Finite strain homogenization using a reduced basis and efficient sampling
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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. To this end, the space of relevant macroscopic stretch tensors is sampled in an efficient manner in order to lower the computational offline costs. Numerical results show speed-up factors in the order of 5-100 and significantly improved robustness while retaining good accuracy. An open-sourced demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.
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