Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations

An FE-DMN method for the multiscale analysis of thermomechanical composites

We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. (Int J Plast 81:18–39, 2016), we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale

Material‐informed training of viscoelastic deep material networks

Deep material networks (DMN) are a data-driven homogenization approach that show great promise for accelerating concurrent two-scale simulations. As a salient feature, DMNs are solely identified by linear elastic precomputations on representative volume elements. After parameter identification, DMNs act as surrogates for full-field simulations of such volume elements with inelastic constituents. In this work, we investigate how the training on linear elastic data, i.e., how the choice of the loss function and the sampling of the training data, affects the accuracy of DMNs for inelastic constituents. We investigate linear viscoelasticity and derive a material-informed sampling procedure for generating the training data and a loss function tailored to the problem at hand. These ideas improve the accuracy of an identified DMN and allow for significantly reducing the number of samples to be generated and labeled

An FE-DMN method for the multiscale analysis of thermomechanical composites

We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. (Int J Plast 81:18–39, 2016), we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale

Efficient two‐scale simulations of microstructured materials using deep material networks

Deep material networks (DMN) are a promising piece of technology for accelerating concurrent multiscale simulations. DMNs are identified by linear elastic pre-computations on representative volume elements, and serve as high-fidelity surrogates for full-field simulations on microstructures with inelastic constituents. The offline training phase is independent of the online evaluation, such that a pre-trained DMN may be applied for varying material behavior of the constituents. In this contribution, we investigate a two-scale component simulation of industrial complexity accelerated by DMNs. To this end, a DMN is solved implicitly at every Gauss point to include the microstructure information into the macro simulation

An FE–DMN method for the multiscale analysis of short fiber reinforced plastic components

In this work, we propose a fully coupled multiscale strategy for components made from short fiber reinforced composites, where each Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN) which covers the different fiber orientation states varying within the component. These DMNs need to be identified by linear elastic precomputations on representative volume elements, and serve as high-fidelity surrogates for full-field simulations on microstructures with inelastic constituents. We discuss how to extend direct DMNs to account for varying fiber orientation, and propose a simplified sampling strategy which significantly speeds up the training process. To enable concurrent multiscale simulations, evaluating the DMNs efficiently is crucial. We discuss dedicated techniques for exploiting sparsity and high-performance linear algebra modules, and demonstrate the power of the proposed approach on an injection molded quadcopter frame as a benchmark component. Indeed, the DMN is capable of accelerating two-scale simulations significantly, providing possible speed-ups of several magnitudes

Trustless, Censorship-Resilient and Scalable Votings in the Permission-based Blockchain Model

Voting systems are the tool of choice when it comes to settle an agreement of different opinions. We propose a solution for a trustless, censorship-resilient and scalable electronic voting platform. By leveraging the blockchain together with the functional encryption paradigm, we fully decentralize the system and reduce the risks that a voting provider, like a corrupt government, does censor or manipulate the outcome

Training deep material networks to reproduce creep loading of short fiber-reinforced thermoplastics with an inelastically-informed strategy

Deep material networks (DMNs) are a recent multiscale technology which enable running concurrent multiscale simulations on industrial scale with the help of powerful surrogate models for the micromechanical problem. Classically, the parameters of the DMNs are identified based on linear elastic precomputations. Once the parameters are identified, DMNs may process inelastic material models and were shown to reproduce micromechanical full-field simulations with the original microstructure to high accuracy. The work at hand was motivated by creep loading of thermoplastic components with fiber reinforcement. In this context, multiple scales appear, both in space (due to the reinforcements) and in time (short- and long-term effects). We demonstrate by computational examples that the classical training strategy based on linear elastic precomputations is not guaranteed to produce DMNs whose long-term creep response accurately matches high-fidelity computations. As a remedy, we propose an inelastically informed early stopping strategy for the offline training of the DMNs. Moreover, we introduce a novel strategy based on a surrogate material model, which shares the principal nonlinear effects with the true model but is significantly less expensive to evaluate. For the problem at hand, this strategy enables saving significant time during the parameter identification process. We demonstrate that the novel strategy provides DMNs which reliably generalize to creep loading

Learning with Errors in the Exponent

We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC\u2705] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over. Most notably are worst-case hardness and post-quantum resistance. In fact, LWEE\u27s duality is due to the reducibility to two seemingly unrelated assumptions: learning with errors and the representation problem [Brands, Crypto\u2793] in finite groups. For suitable parameter choices LWEE superposes properties from each individual intractability problem. The argument holds in the classical and quantum model of computation. We give the very first construction of a semantically secure public-key encryption system in the standard model. The heart of our construction is an ``error recovery\u27\u27 technique inspired by [Joye-Libert, Eurocrypt\u2713] to handle critical propagations of noise terms in the exponent