3 research outputs found
Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling
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.Comment: 28 page
On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling
A multi-fidelity surrogate model for highly nonlinear multiscale problems is
proposed. It is based on the introduction of two different surrogate models and
an adaptive on-the-fly switching. The two concurrent surrogates are built
incrementally starting from a moderate set of evaluations of the full order
model. Therefore, a reduced order model (ROM) is generated. Using a hybrid
ROM-preconditioned FE solver, additional effective stress-strain data is
simulated while the number of samples is kept to a moderate level by using a
dedicated and physics-guided sampling technique. Machine learning (ML) is
subsequently used to build the second surrogate by means of artificial neural
networks (ANN). Different ANN architectures are explored and the features used
as inputs of the ANN are fine tuned in order to improve the overall quality of
the ML model. Additional ANN surrogates for the stress errors are generated.
Therefore, conservative design guidelines for error surrogates are presented by
adapting the loss functions of the ANN training in pure regression or pure
classification settings. The error surrogates can be used as quality indicators
in order to adaptively select the appropriate -- i.e. efficient yet accurate --
surrogate. Two strategies for the on-the-fly switching are investigated and a
practicable and robust algorithm is proposed that eliminates relevant technical
difficulties attributed to model switching. The provided algorithms and ANN
design guidelines can easily be adopted for different problem settings and,
thereby, they enable generalization of the used machine learning techniques for
a wide range of applications. The resulting hybrid surrogate is employed in
challenging multilevel FE simulations for a three-phase composite with
pseudo-plastic micro-constituents. Numerical examples highlight the performance
of the proposed approach