Abstract:
In the first part of my talk, I will present a hybrid data-physics driven reduced-order homogenization (dpROH) approach for efficient analysis of fiber reinforced composites. The dpROH improves the accuracy of the physics-based approaches, but retains its unique characteristics, such as interpretability and extrapolation. In the second part of my talk, I will present a hybrid data-physic driven computational framework for high-volume resin transfer molding (HV-RTM) of fiber reinforced composites. Due relatively high speed of resin flow and significant convective effects, the hybrid data-physics drive approach efficiently solves the nonlinear steady-state Navier-Stokes equations rather than the linear Stokes equations commonly adopted for the simulation of classical resin transfer molding processes.
Bio:
Dr. Fish is the Carleton Professor and Chair of the Department of Civil Engineering and Engineering Mechanics at Columbia University. He is a Founder and Director of Columbia University initiative for Computational Science and Engineering (iCSE) involving 80 faculty from multiple schools. Dr. Fish is a recipient of the John von Neumann Medal from USACM for "sustained and seminal contributions to the field of multiscale computational science and engineering and for its major impact on industry” and the Grand Prize from the Japan Society for Computational Engineering and Science among numerous other awards. Dr. Fish is a two-term past President of the United States Association for Computational Mechanics (USACM) and currently serves as the Vice-President of the International Association for Computational Mechanics. Dr. Fish is a Founder and Editor-in-Chief of the International Journal of Multiscale Computational Engineering, an Editor of the International Journal for Numerical Methods in Engineering and serves on the editorial board of several journals.
Summary:
Focus: Digital Twins for complex physical systems
Computational challenges:
Example: injecting resin into mold to create parts
Flow: rate depends on pressure non-linearly
Solids
Scale mixing
High range of reynolds numbers
High gradient (changing quickly over space)
Multiphysics at multiple scale
Different physical processes coupled at microscopic scale
Data-physics driven multiscape approach for high-pressure resin transfer molding
Molding parts of large devices (cars) quickly and reliably
We have a mold
Inject resin into the mold at high pressure
Cure the resin
Model: Navier-Stokes fluid flow
Single-phase saturated flow model
Two-scale composite
Non-linear relation between average velocity and pressure gradient
Non-linear map from micro-scale finite volumes to macro-scale mold’s behavior
Unique solution: given pressure gradient one can uniquely determine average velocity and instantaneous permeability
Thus, can train a neural surrogate of these two bi-variate relationships (99.9% accuracy after 5 minutes training)
3-scale model
Microscale representative volume: porous medium
Mesoscale representative volume: fluid, with history dependence
Macroscale
Fit a neural surrogate to this 3-scale model with high accuracy (different nets for the scales)
Reduced Order Homogenization for component analysis
We have a solid that has been cured curing manufacturing
Transformation field analysis
Fine-scale train can be computed from the coarse scale strain
Small changes in volume/strain induces a deviation in shape
Need to compute the eigen-strains:
independent types of macro deformations and how they affect the micro-state
Eigen-strains need to be discretized
Inference of eigen-strains
Trained a Recurrent neural network (GRU) on high-fidelity model of the micro behavior
Several runs of high-fidelity model produces the history of the process, which simplifies the training process
Bayesian inference uses neural network model to optimize
Produces a high-quality model with good values of free parameters
Coupled Chemo-Thermo-Mechanical Multiscale model for predicting effects of manufacturing on the product
Interactions among:
Temperature-induced crystallization
Thermal strains
Effective material properties
Multi-scale approach makes it possible to predict defects in micro-structure (prior work could only predict for macro-structure)
Was used to model impacts on car bodies, which enables GM to use lighter materials
Summary:
Data-driven physics multi-scale model can approximate Navier Stokes well
Multi-phase and multi-scale modeling is needed to account for all the phenomena with resins
Prediction: integrated multi-scale analysis tools for digital twins will become practically used in 5-7 years
Observations:
In using data-driven models, start with simple approaches
Few parameters
Phenomenological
Data-driven approximations work best when solutions are unique
When the model is history-dependent the training challenge is much larger
Good use-case: model reduction
Analytic and data driven models need to be validated using experimental data in similar