In this work, a hybrid physics-based data-driven surrogate model for the microscale analysis of heterogeneous material is investigated. The proposed model benefits from the physics-based knowledge contained in the constitutive models used in the full-order micromodel by embedding the material models in a neural network. Following previous developments, this paper extends the applicability of the physically recurrent neural network (PRNN) by introducing an architecture suitable for rate-dependent materials in a finite strain framework. In this model, the homogenized deformation gradient of the micromodel is encoded into a set of deformation gradients serving as input to the embedded constitutive models. These constitutive models compute stresses, which are combined in a decoder to predict the homogenized stress, such that the internal variables of the history-dependent constitutive models naturally provide physics-based memory for the network. To demonstrate the capabilities of the surrogate model, we consider a unidirectional composite micromodel with transversely isotropic elastic fibers and elasto-viscoplastic matrix material. The extrapolation properties of the surrogate model trained to replace such micromodel are tested on loading scenarios unseen during training, ranging from different strain-rates to cyclic loading and relaxation. Speed-ups of three orders of magnitude with respect to the runtime of the original micromodel are obtained.

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Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite element analysis (FE²) due to the exceedingly high computational costs often associated with it and the high number of similar micromechanical analyses involved. To tackle the issue, using surrogate models to approximate the microscopic behavior and accelerate the simulations is a promising and increasingly popular strategy. However, several challenges related to their data-driven nature compromise the reliability of surrogate models in material modeling. The alternative explored in this work is to reintroduce some of the physics-based knowledge of classical constitutive modeling into a neural network by employing the actual material models used in the full-order micromodel to introduce non-linearity. Thus, path-dependency arises naturally since every material model in the layer keeps track of its own internal variables. For the numerical examples, a composite Representative Volume Element with elastic fibers and elasto-plastic matrix material is used as the microscopic model. The network is tested in a series of challenging scenarios and its performance is compared to that of a state-of-the-art Recurrent Neural Network (RNN). A remarkable outcome of the novel framework is the ability to naturally predict unloading/reloading behavior without ever seeing it during training, a stark contrast with popular but data-hungry models such as RNNs. Finally, the proposed network is applied to FE² examples to assess its robustness for application in nonlinear finite element analysis.

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This paper presents BIOS (acronym for Biologically Inspired Optimization System), an object-oriented framework written in C++, aimed at heuristic optimization with a focus on Surrogate-Based Optimization (SBO) and structural problems. The use of SBO to deal with structural optimization has grown considerably in recent years due to the outstanding gain in efficiency, often with little loss in accuracy. This is especially promising when adaptive sampling techniques are used. However, many issues are yet to be addressed before SBO can be employed reliably in most optimization problems. In that sense, continuous experimentation, testing and comparison are needed, which can be more easily carried out in an existing framework. The architecture is designed to implement conventional nature inspired algorithms and Sequential Approximated Optimization (SAO). The system aims to be efficient, easy to use and extensible. The efficiency and accuracy of the system are assessed on a set of benchmarks, and on the optimization of functionally graded structures. Excellent results are obtained.@en

In a concurrent (FE2) multiscale modeling is an increasingly popular approach for modeling complex materials. As such, it is especially suited for modeling composites, as their complex microstructure can be explicitly modeled and nested to each integration point of the macroscale. However, this generality is often associated with exceedingly high computational costs for real-scale applications. One way to tackle the issue is to employ a cheaper-to-evaluate surrogate model for the microstructure based on few observations of the high-fidelity solution. On this note, Neural Networks (NN) are by far the most popular technique in building constitutive surrogates. However, conventional NNs assume a unique mapping between strains and stresses, limiting their ability to reproduce path-dependent behavior. Moreover, their data-driven nature severely limits their ability to extrapolate away from their training spaces. To circumvent these drawbacks, the alternative explored in this work is to reintroduce some of the physics-based knowledge of the problem into the NN. This is done by employing actual material models used in the full-order micromodel as the activation function of one of the layers of the network. Thus, path-dependency arises naturally since every material model in the layer has its own internal variables. To assess its capabilities, the network is employed as the surrogate model for a composite Representative Volume Element with elastic fibers and elasto-plastic matrix material. First, for a single micromodel, the performance of the network is compared to that of a state-of-the-art Recurrent Neural Network (RNN) in a number of challenging scenarios for data-driven models. Then, the proposed framework is applied to an FE2 example and the results are compared to the full-order solution in terms of accuracy and computational cost. An important outcome of the physics-infused network is the ability to naturally predict unloading/reloading behavior without ever seeing it during training, a stark contrast with highly popular but data-hungry models such as RNN. @en

This work presents an efficient methodology for the optimum design of functionally graded structures using a Kriging-based approach. The method combines an adaptive Kriging framework with a hybrid particle swarm optimization (PSO)algorithm to improve the computational efficiency of the optimization process. In this approach, the surrogate model is used to replace the high-fidelity structural responses obtained by a NURBS-based isogeometric analysis. In addition, the impact of key factors on surrogate modelling, as the correlation function, the infill criterion used to update the surrogate model, and the constraint handling is assessed for accuracy, efficiency, and robustness. The design variables are related to the volume fraction distribution and the thickness. Displacement, fundamental frequency, buckling load, mass, and ceramic volume fraction are used as objective functions or constraints. The effectiveness and accuracy of the proposed algorithm are illustrated through a set of numerical examples. Results show a significant reduction in the computational effort over the conventional approach.@en