Microstructure-guided deep material network for rapid nonlinear material modeling and uncertainty quantification

Tianyu Huang

doi:10.1016/j.cma.2022.115197

2022-08-01

DOI：10.1016/j.cma.2022.115197

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Modeling nonlinear materials with arbitrary microstructures and loading paths is crucial in structural analyses with heterogeneous materials with uncertainty. However, it is computationally prohibitive because (1) fine meshes are required to resolve the microstructures for nonlinear simulations, (2) enormous model evaluations are expected to simulate stochastic microstructures and the loading variabilities, and (3) nonlinear material models are generally expensive to solve. In this paper, we present the microstructure-guided deep material network (MgDMN), a deep-learning-based approach to model multi-phase materials and efficiently predict their mechanical response under virtually any loading paths and microstructure definitions considering plasticity. This work is built upon the earlier development of the deep material network (DMN) method for fast predictions of nonlinear homogenized responses of multi-phase materials using linear elastic training data for a predefined microstructure. We extend DMN to MgDMN for any microstructure definition by parameterizing the microstructure space, mapping a small set of DMNs to their respective microstructure parameters, and interpolating the DMNs to generate new models in the microstructure space. The proposed method achieves superb efficiency and accuracy since the interpolated DMNs do not need additional training to predict nonlinear behavior of any new microstructures. We demonstrate our approach via modeling and uncertainty quantification of short fiber reinforced polymer (SFRP) composites. We show that for this dual-phase material, only four base DMNs are needed to predict the nonlinear stress responses for any loading path given any fiber volume fraction, orientation states, and constituent properties as long as the combination is within the microstructure space enclosed by the base models. The accelerated modeling process enables complex structural simulations of heterogeneous materials and nonlinear stochastic analyses with uncertain microstructures, which are essential in computational materials engineering and multiscale modeling. Our research also draws insights into the impact of microstructure uncertainties on linear and nonlinear material behaviors. (c) 2022 Elsevier B.V. All rights reserved.

Keyword:

Material modeling

Nonlinear materials

Microstructural analysis

Deep learning

Uncertainty quantification

Short fiber composites