Neural-network acceleration of projection-based model-order-reduction for finite plasticity: Application to RVEs

Abstract

Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively. Consequently, no stiffness matrix needs to be constructed and the stress update needs to be computed only once per increment. In this contribution, a recurrent neural network is developed to accelerate a projection-based model-order-reduction of the elastoplastic mechanical behaviour of an RVE. In contrast to a neural network that merely emulates the relation between the macroscopic deformation (path) and the macroscopic stress, the neural network acceleration of projection-based model-order-reduction preserves all microstructural information, at the price of computing this information once per increment.

Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics

“…Another possible extension is to consider a much wider class of phenomena and models, including buckling instabilities and more general history/time-dependent phenomena (visco-elasticity, dynamics, plasticity, etc. ), which would allow tackling more challenging problems in solid mechanics, see e.g., (Vijayaraghavan et al, 2021). Going beyond mechanics, these approaches can be also adopted for a much wider range of engineering and scientific applications.…”

“…The first approach relies on enhancing the DL model with the information on underlying physics-an approach popularly termed as Physics Informed Neural Networks (PINN) (McFall and Mahan, 2009;Mao et al, 2020;Samaniego et al, 2020;Odot et al, 2022). The second approach includes the underlying physics implicitly, through high-fidelity simulations done in silico to provide the necessary amount of synthetically generated data, which has shown to be useful in various applications (Le et al, 2017;Aydin et al, 2019;Pfeiffer et al, 2019;Vijayaraghavan et al, 2021;Kim et al, 2022). In this work, we will follow the latter approach and will focus on DL surrogate models that are trained on synthetically generated data from finite element simulations in non-linear elasticity.…”

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

“…Alternatively, artificial neural networks (ANNs) may be used for approximating the effective elastic energy of nonlinear elastic media [36][37][38] or the stress-strain relationship of inelastic materials [39][40][41]. Moreover, ANNs and reduced-order models may be combined on the fly [42,43]. ANN-based approaches typically suffer when evaluated far away from the training set.…”