A Stochastic FE² Data-Driven Method for Nonlinear Multiscale Modeling

Area of Science:

• Computational mechanics
• Materials science
• Machine learning

Background:

• Multiscale modeling is crucial for understanding heterogeneous materials.
• Traditional methods for nonlinear multiscale calculations are computationally intensive.
• Accurate surrogate models are needed to reduce computational cost.

Purpose of the Study:

• To introduce a stochastic data-driven multilevel finite-element (FE2) method for random nonlinear multiscale calculations.
• To develop a hybrid neural-network-interpolation (NN-I) scheme for constructing surrogate models.
• To demonstrate the application of this machine learning method for uncertainty quantification.

Main Methods:

• A hybrid neural-network-interpolation (NN-I) scheme was developed to create a surrogate model for macroscopic nonlinear constitutive laws.
• Representative volume element calculations provided input data for the surrogate model.
• The developed FE2 method integrates the NN-I scheme to replace direct nonlinear multiscale calculations.

Main Results:

• The NN-I scheme enhanced surrogate model accuracy, especially with limited data.
• Computational time was reduced by several orders of magnitude compared to direct FE2.
• The method enabled Monte Carlo simulations for uncertainty propagation in nonlinear heterogeneous structures.

Conclusions:

• The proposed data-driven FE2 method offers a computationally efficient approach for nonlinear multiscale problems.
• This machine learning technique facilitates uncertainty quantification and probabilistic model identification.
• Successful application to nonlinear electric conduction in graphene-polymer composites demonstrates its practical utility.