An efficient solver for large-scale linear FE simulations was extended for nonlinear material behavior. The material model included damage-based tissue degradation and fracture. The new framework was applied to 20 trabecular biopsies with a mesh resolution of 36 μm. Suitable material parameters were identified based on two biopsies by comparison with axial tension and compression experiments. The good parallel performance and low memory footprint of the solver were preserved. Excellent correlation of the maximum apparent stress was found between simulations and experiments (R 2 > 0.97). The development of local damage regions was observable due to the nonlinear nature of the simulations. A novel elasticity limit was proposed based on the local damage information. The elasticity limit was found to be lower than the 0.2% yield point. Systematic differences in the yield behavior of biopsies under apparent compression and tension loading were observed. This indicates that damage distributions could lead to more insight into the failure mechanisms of trabecular bone.

We generalize the inverse patchy colloid model that was originally developed for heterogeneously charged particles with two identical polar patches and an oppositely charged equator to a model that can have a considerably richer surface pattern. Based on a Debye-Hückel framework, we propose a coarse-grained description of the effective pair interactions that is applicable to particles with an arbitrary patch decoration. We demonstrate the versatility of this approach by applying it to models with (i) two differently charged and/or sized patches, and (ii) three, possibly different patches.

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Thermal simulations are an important part in the design of electronic systems, especially as systems with high power density become common. In simulation-based design approaches, a considerable amount of time is spent by repeated simulations. In this work, we present a proof-of-concept study of the application of convolutional neural networks to accelerate those thermal simulations. The goal is not to replace standard simulation tools but to provide a method to quickly select promising samples for more detailed investigations. Based on a training set of randomly generated circuits with corresponding Finite Element solutions, the full 3D steady-state temperature field is estimated using a fully convolutional neural network. A custom network architecture is proposed which captures the long-range correlations present in heat conduction problems. We test the network on a separate dataset and find that the mean relative error is around 2 % and the typical evaluation time is 35 ms per sample ( 2 ms for evaluation, 33 ms for data transfer). The benefit of this neural-network-based approach is that, once training is completed, the network can be applied to any system within the design space spanned by the randomised training dataset (which includes different components, material properties, different positioning of components on a PCB, etc.).