Chen's research interests are in computational solid mechanics and multiscale materials modeling. More specifically, he investigates:
Finite Element and Meshfree Methods for nonlinear mechanics
Multiscale modeling of material defects
Computational methods for simulation of fragment-impact processes
Computational shock dynamics
Physics constrained data-driven computing with applications to biological materials and digital twins
Physics-Informed manifold learning with deep autoencoders for nonlinear materials
Thermodynamically consistent machine-learned material models for path-dependent materials
Reduced order methods for biological systems
Reduced order method for inelastic materials and materials with defects
Multiscale and reduced order modeling of molecular systems with applications to DNA modeling
Image based multiscale computational mechanics for skeletal muscles
Accelerated Reproducing Kernel Particle Method for continuum, plates, shells, composites, large deformation, and contact problems
Mathematical analysis of Galerkin and collocation meshfree methods
Computational methods development for modeling of material manufacturing processes such as metal forming, stamping, and extrusion
Wavelet Galerkin method in multiscale homogenization of heterogeneous materials
Mesoscopic modeling of grain growth and grain boundary migration
Adaptive multiscale meshfree method for solving Schrödinger equation in quantum mechanics
Modeling of microstructural evolution and local instability (such as wrinkling formation) in polycrystalline materials
Computational damage mechanics and strain localization
Computational methods for rubber-like incompressible materials
Arbitrary Lagrangian Eulerian method for large deformation and contact problems
Mixed finite element method based on multiple-field variational principle
Probabilistic finite element method for acoustic-structure interaction
Machine-Learning Enhanced Data-Driven Computing
Physics-Informed Manifold Learning with Deep Autoencoders for Nonlinear Materials [Q. He, X. He]
The recent advancements in machine learning algorithms and data-driven computing offer new opportunities for the modeling multi-scale, multi-physics complex problems in science and engineering. We developed a physics-informed data-driven constitutive modeling approach by integrating physical constraints, such as energy convexity and objectivity, into data-driven constitutive modeling. To counteract high-dimensionality issues and presented noise in data, autoencoders are employed to learn an essential low-dimensional representation of data, from which the mechanisms governing the evolution of path-dependent deformation are extracted and integrated into data-driven path-dependent constitutive predictions for enhanced robustness and accuracy.
An application of proposed computational technology is the data-driven constitutive modeling of bio-tissues, which is shown in the above figure.
Thermodynamically Consistent Machine-Learned Material Models for Path-Dependent Materials [X. He]
A machine-learned, physics-informed data-driven constitutive modeling approach has been developed for path-dependent materials based on the measurable material states. The proposed data-driven constitutive model is designed with the consideration of universal thermodynamics principles, where the Internal State Variables (ISV) essential to the material path-dependency are inferred automatically from the hidden state of Recurrent Neural Networks (RNN). The RNN describing the evolution of the data-driven machine-learned ISVs follows the thermodynamics second law.
The effectiveness of the proposed method is evaluated by a verification using a synthetic elastoplastic model data as shown on the right of the figure, and a soil material under cyclic shear loading as shown on the left of the figure above.
Hyper Reduction of Nonlinear Inelastic Materials [S. Kaneko, H. Wei, Q. He]
Simulations of the nonlinear mechanical deformation processes of materials subjected to thermal cycling with high-fidelity numerical models often demand high computational costs due to material nonlinearities and long thermal loading period. To accelerate such thermal cycling simulation, an efficient hyper-reduction method is introduced to avoid the full domain integration during the elastoplastic online simulation. With a Gappy-POD approach, only a few components of tangent stiffness matrix and internal force vector associated with degrees of freedom identified by the greedy algorithm need to be calculated to form the reduced-order discrete equation via a POD projection.
In a thermal fatigue life prediction of a flip chip assembly shown below with the hyper-reduction method, only 4.6% CPU time is consumed with 3.9% error compared to the high fidelity model.
Multi-Scale Machine Learning Enhanced Data-Driven Musculoskeletal Digital Twins [K. Taneja, X. He, Q. He]
Identification of muscle-tendon force generation properties and muscle activities from physiological measurements, e.g., motion data and raw surface electromyography (sEMG), offers opportunities to construct a subject-specific musculoskeletal (MSK) digital twin system for health condition assessment and motion prediction. In this work as shown in the figure, a feature-encoded physics-informed parameter identification neural network (FEPI-PINN) was developed for simultaneous prediction of motion and parameter identification of human MSK systems. This FEPI-PINN model can be trained to relate sEMG signals to joint motion and simultaneously identify key MSK parameters. The developed framework can effectively identify subject-specific muscle parameters and the trained physics-informed forward-dynamics surrogate, which yields accurate motion predictions of elbow flexion-extension motion that are in good agreement with the measured joint motion data.
Neural Network Enhanced RKPM for for Modeling Localization and Microstructural Evolution [J. Baek, K. Susuki]
The microscopic behaviors of materials under large deformation often entail complicated localized phenomena and micro-damage. To accurately model localizations, such as plastic slip, grain boundary evolution/migration and micro-shearband, requires highly refined discretization, which significantly increases the computational cost. While adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh-based methods to perform adaptive model refinement. A neural network-enhanced reproducing kernel particle method (NN-RKPM) is proposed, where RK approximation is utilized to approximate the smooth part of the solution while the location, orientation and shape of the solution transition is automatically captured by the NN approximation by the minimization of total potential energy.
The proposed computational framework has been applied to modeling grain refinement mechanisms by coupling the proposed NN-RKPM with phase field and Cosserat crystal plasticity, including the migration of grain boundaries at a triple junction and sub-grain formation of a material with activated slip systems, for validating the effectiveness of the proposed methods.
Digital Models for Disasters Prediction and Mitigation
A Semi‑Lagrangian RKPM with Particle‑Based Shock Algorithm for Explosive Welding and Jet Formation Simulation [J. Baek]
The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the volumetric strain energy to accurately embed the key shock physics in the absence of a mesh or grid.
The figures on the left are the progressive explosive welding processes involving shocks, jet formation, and smooth-to-wavy interface morphology transition. As shown on the right of the figure, numerical results show good agreement with experimental results (Bahrain, A. S., & Grassland, B. (1964)).
A Variational Multiscale Immersed Meshfree (VMIM) Method and Shock Algorithms for Modeling of Fluid Structure Interactive Systems Involving Shock Waves [T. Huang, F. Beckwith]
An immersed meshfree RKPM under a variational multiscale framework for modeling fluid–structure interactive (FSI) systems involving shock waves was developed. The proposed method enables flexible non-body-fitted discretization, approximations, and quadrature rules for solid and fluid subdomains. In the proposed approach, the fictitious fluid is combined with the foreground solid, forming an “effective solid problem” solved on a moving foreground domain, while the background fluid problem is solved with prescribed solid velocity in the overlapping domain to reduce the leaking instability and mesh sensitivity.
The demonstration problems above show good agreement between numerical and experimental results: flexible panel under a shock wave (left), concrete slab under detonation (middle) and shock waves interacting with a rigid wedge (right).
A Deformation‑Dependent Coupled Lagrangian/Semi‑Lagrangian Meshfree Hydromechanical Formulation for Landslide Modeling [J. Baek, R. Schlinkman, H. Wei]
In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and the semi-Lagrangian (reproducing kernel SL-RK) approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. A ramp function is constructed based on the equivalent plastic strain, which serves as a deformation-dependent transition from L-RK to SL-RK shape functions as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed u-P formulation to couple the solid and fluid phases.
Demonstration problems in the figure above show the coupled Lagrangian/semi-Lagrangian reproducing kernel (L-SL RK) modeling of collapse of a granular column (left) and a seepage-induced levee failure (right).
Soft Target Impact Modeling by Smooth Kernel Contact Algorithms [R. Schlinkman, J. Baek]
The study of the impact of projectiles into soft targets such as water and soil is of great importance in the defense industry. Interest lies in the depth of penetration and/or the deformation of the projectile. However, the extreme deformation of both projectile and target materials such as fracture and fragmentation and the complicated projectile-target interaction can make modelling such events difficult if one uses a mesh-based method, such as the finite element method (FEM). In this research, we combine the RK smooth contact formulation which can successfully model complex rough/smooth contact surfaces with a coupled Lagrangian/semi-Lagrangian (L-SL) formulation which is able to model extreme deformation scenarios without the need for remeshing while minimizing the computational cost.
Demonstration problems in the figure above show an ogive-nose projectile penetrating into soil and accurately matching theoretical and experimental results (left) and a hollow-nose projectile impacting soil causing large deformation in the projectile and scattering of the soil (right).
Support Vector Machine Guided Reproducing Kernel Particle Method for Image-Based Modeling of Microstructures [Y. Wang, J. Baek]
The composition of multiple materials can combine the merits of individual materials to produce composites with enhanced mechanical properties such as higher strength and reduced weight than the individual constituents. Modeling heterogeneous materials has remained challenging for mesh-based methods discretized with body-fitted discretization and meshfree methods formulated with smooth approximations. In the first part of this work, an Interface-Modified Reproducing Kernel Particle Method (M-RKPM) is proposed within the context of meshfree methods for effective approximations of weak discontinuities. The proposed method scales the smooth kernel functions with a regularized heavy-side function with respect to the material interfaces to alleviate Gibb's oscillations. This M-RKPM is formulated without additional degrees of freedom associated with the interface nodes commonly needed in the conventional treatment of weak discontinuities in the meshfree methods. Moreover, M-RKPM can be implemented with kernel functions of arbitrary smoothness at the interface locations and with various domain integration techniques, such as Gauss numerical integration (GI) and Smoothed Conforming Nodal Integration (SCNI). The second part of this work deals with composite structures with complex microstructures segmented from Micro-CT images. The support vector machine (SVM) and variational level set method are adopted to automate the discretization and approximation of composite microstructures.
The left part of the above image presents the material ID identification, adaptive nodal refinement, and interface node identification through the reproducing kernel (RK) filtering using RK shape functions and threshold filtering, as well as through the Support Vector Machine (SVM) algorithms for image segmentation. The right part of the above image illustrates a preliminary normal strain approximation result simulated directly using the Micro-CT scan of the Epoxy-alumina composite sample, based on RKPM without any interface treatments.
Multi-Physics Computational Models for Coupled-Systems
Imaged-based RKPM for Chemo-Mechanical Modeling of Energy Storage Materials [K. Susuki]
Kristen is collaborating with the National Renewable Energy Laboratory (NREL) to develop meshfree electrochemical-mechanical system degradation models with applications to batteries, electrolyzers, and fuel-cells. Since many of these energy storage materials undergo significant charge cycling, understanding their reliability and durability is fundamental in predicting their performance after long-term operation. With microstructural images supplied by NREL, image-based modeling techniques are used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electrochemical-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in capturing crack propagation due to mesh dependency. The Reproducing Kernel Particle Method (RKPM)—a meshfree method—and machine learning techniques are leveraged to accurately capture crack propagation throughout the material, as well as to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.
The figure above demonstrates some numerical simulation results of multi-grain microstructure deformations.
Physics-Informed Data-Driven Constitutive Modeling of Thermo-Hydro-Mechanical Behaviors of Bentonite under High Temperature [J. Baek, X. He]
When used as buffer material between radioactive waste canisters and the surrounding host rock in deep geological repositories, bentonite can undergo extreme temperatures higher than 200 °C. In this research project, we focus on developing a physics-based data-driven computational framework for modeling the thermo-hydro-mechanical (THM) behavior of bentonite in the high-temperature regime that has not been well-discovered. The challenge in modeling the complicated temperature/saturation/deformation-dependent THM constitutive behavior is addressed by thermodynamically consistent machine-learned (TCML) models. The TCML models are incorporated with an advanced RKPM THM modeling framework that is additionally developed in this research project.
The figure above shows the training and testing errors of the machine-learned soil-water retention curve (ML-SWRC) (left) and a tank-scale simulation result computed by RKPM with ML-SWRC, compared with the experimental data (right).
Isogeometric Analysis and Shape Optimization
Automated isogeometric analysis and design optimization for complex shell structures [H. Zhao]
It is well-established that the analysis bottleneck in exploring geometrical design spaces is mesh generation. The field of isogeometric analysis (IGA) aims to directly analyze spline-based geometry representations used in computer-aided design (CAD) programs, bypassing mesh generation entirely. This research project develops an open-source Python framework named PENGoLINS for penalty coupling of non-matching Kirchhoff--Love shells. PENGoLINS uses FEniCS and tIGAr to automate the computation of Gateaux derivatives and IGA. The framework generates topologically-1D, geometrically-2D quadrature meshes in the spline parameter space to integrate coupling terms that penalize deviations from displacement and rotational continuity at the geometric intersections between separately parametrized spline patches. PENGoLINS makes structural analysis straightforward for CAD models consisting of multiple NRUBS surfaces. The seamless integration between CAD and analysis models in IGA makes it a natural choice for design optimization. The updated design in the optimization process can be precisely captured in the analysis, which in turn ensures accurate responses due to the exact geometry representation and excellent approximation capabilities of spline basis functions. The shape of the shell structure is updated through a trivariate B-spline free-form deformation (FFD) block, which encompasses the entire shell structure, to minimize an objective function. The FFD block modifies the Lagrange control points of all shell patches concurrently to preserve the surface–surface intersections, and the resulting NURBS surfaces of shells are obtained using the Lagrange extraction technique.
The figure above shows the streamlined workflow from geometry design, structural analysis, and design optimization for an electric vertical takeoff and landing (eVTOL) aircraft wing using IGA.