Research

1. Data-efficient machine learning

Overview: As AI and machine learning (ML) technologies transform the engineering landscape, data-efficient modeling has become essential for advancing composite modeling. Advanced ML methods (e.g., neural networks (NN)) require large training datasets, which is often impractical for composites due to the high cost of experiments and simulations. Dr. Liu’s team is developing hybrid NN-finite element (FE) frameworks [1-3], transfer learning [4], physics-guided NN [5], and physical coding [6] techniques that drastically reduce data-generation costs while maintaining high prediction accuracy.

Significance and Impact: This research bridges the gap between AI/ML technology and materials and structural engineering, enabling practical and scalable ML applications in composites design and performance prediction. Developing data-efficient ML models can accelerate innovations in aerospace, defense, and energy sectors, where data scarcity has long hindered the deployment of AI/ML-driven modeling.

Current Focus Areas:

  • Develop transfer learning models for multiscale modeling of composites (supported by NSF, PI).
  • Physical encoding for multiscale modeling of microstructured materials.
Examples of data-efficient ML modeling for advanced materials and structures

Reference:

  1. Liu, X.*, Tao, F. and Yu, W. 2020. A neural network enhanced system for learning nonlinear constitutive relation and failure criterion of fiber reinforced composites, Composite Structures, 252(15), p.112658. DOI: 10.1016/j.compstruct.2020.112658
  2. Liu, X.*, Tao, F., Du, H., Yu, W. and Xu, K., 2020. Learning nonlinear constitutive laws using neural network models based on indirectly measurable data, Journal of Applied mechancis, 87(8), p.081003 DOI: 10.2514/1.J058765
  3. Tao, F.*, Liu, X., Du, H. and Yu, W., 2021. Learning composite constitutive laws via coupling Abaqus and deep neural network. Composite Structures, p.114137. DOI: 10.1016/j.compstruct.2021.114137
  4. Liu, X.*, Liu, B., Tian, S. and Yu, W., 2024. Analysis of Tow-steered Laminates of Composites Using a Mixed-fidelity Neural Network Model. In AIAA SCITECH 2024 Forum (p. 0266).
  5. Liu, B., Costa, S., Liu, X.*, Wilhelmsson, D., and Jia, X., 2025, Convolutional neural network for predicting mechanical behavior of composites with fiber waviness, Composites part A: Applied Science and Manufacturing, 188, 108574. DOI: 10.1016/j.compositesa.2024.108574
  6. Mazumder, A. and Liu, X.*, 2005. Accelerating Machine Learning-Assisted Multiscale Modeling by Physics-Based Microstructure Encoding. In Proceedings of the American Society for Composites—40th Technical Conference, 10/5-10/8, Dayton, OH.

2. Sectionally reinforced lattice metamaterials

Overview: the advances in additive manufacturing (AM) have enabled advanced lattice metamaterails with engineered microstructures to achieve unprecedented mechanical and multifunctional behaviors. Instead of focusing on the topology of the microstructures, Dr. Liu’s team pioneered the concept of sectionally reinforced beam lattices, achieving up to four- to six-fold improvements in stiffness, strength, and energy absorption compared to conventional designs [1-3]. This breakthrough established a new class of beam lattices, revealing an energy-dissipation mechanism previously unreported in the literature. 

Significance and Impact: The new lattice design introduces sectional reinforcements that differ fundamentally from existing AM lattice designs. Beyond mechanical enhancement, the design also provides a new approach for multifunctional materials, enabling improved mechanical, thermal and acoustic properties that conventional lattices cannot achieve. Lightweight, high-performance materials are key enablers for safer and more sustainable transportation systems. The developed lattices support the creation of lightweight, impact-resistant structural components for AAM landing gear and airframe structures, as well as protective systems for defense applications. Their tunable properties open opportunities in biomedical implants and cushioning materials, where controlled energy absorption and multifunctionality are highly desirable. 

Current Focus Areas:

  • Sectionally reinforced beam lattice for reuseable energy-absorbing structural components of AAM aircrafts (supported by NASA, PI)
  • Energy-absorbing behaviors under dynamic loading
  • Multi-functional sectionally reinforced lattice metamaterials
Quasi-static compression of reinforced Ibeam lattices and two-step energy dissipation mechanism

Reference:

  1. Liu, X.*, Kobir, M.H., Yang, Y., Jiang, F. and Kothari, T., 2023. Improving stiffness and strength of body-centered cubic lattices with an I-shape beam cross-section. Mechanics of Materials, 182, p.104665. DOI: 10.1016/j.mechmat.2023.104665
  2. Kobir, M., Liu, X., and Yang, Y., 2023, Additive manufacturing of body-centered cubic metamaterials with novel I-shaped beam lattice towards enhanced mechanical properties, Manufacturing Letter, 35, 509-515. DOI: 10.1016/j.mfglet.2023.08.004
  3. Kothari, T., Liu, X.*, Kobir, M.H., Yang, Y. and Tao, F., 2025. Design and analysis of reinforced I-beam body-centered cubic lattices for enhanced energy absorption. Composite Structures, 355, 118841. DOI: 10.1016/j.compstruct.2025.118841

3. Machine Learning-Assisted Material and Structure Modeling

Overview: ML-assisted modeling provides a cost-effective alternative to conventional FE-based modeling. Dr. Liu’s team has developed different ML models for design and analysis of textile composites [1-4], composites failure analysis [5-6], and real-time property evaluation of AM materials [7-9]. In collaboration with academic and industry partners, the team is actively investigating emerging ML/AI techniques to overcome long-standing computational bottlenecks in the multiscale modeling and design of advanced materials and structural systems.

Significance and Impact: ML-assisted modeling is reshaping the future of engineering innovation. By integrating advanced AI techniques with fundamental mechanics, this research direction unlocks unprecedented speed, accuracy, and design freedom in analyzing complex composite and AM materials. The AIM³ Lab is at the forefront of this transformation that develops ML/AI models to dramatically reduce simulation time and open new possibilities for optimizing next-generation aerospace and mechanical systems. These breakthroughs directly support industry needs for lighter, safer, and more efficient structures while empowering researchers and engineers to explore vast design spaces that were previously out of reach.

Current Focus Areas:

  • ML/AI-driven tool development for multiscale material and structural modeling (supported by NSF, PI)
  • ML-assisted multiscale modeling of textile composites (supported by AFRL, Co-PI)
  • Exploring new ML/AI techniques (e.g., neural operator, LLMs, foundational models) in material modeling
Some examples of ML-assisted modeling and software development

Reference:

  1. Liu, X.*, Gasco, F., Goodsell, J. and Yu, W., 2019. Initial failure strength prediction of woven composites using a new yarn failure criterion constructed by deep learning. Composite Structures, 230, p.111505. DOI: 10.1016/j.compstruct.2019.111505
  2. Liu, X.*, Peng, B. and Yu, W., 2021. Multiscale modeling of the effective thermal conductivity of 2D woven composites by mechanics of structure genome and neural networks. International Journal of Heat and Mass Transfer, 179, p.121673. DOI: 10.1016/j.ijheatmasstransfer.2021.121673
  3. Liu, X.*, Zhou, X.Y., Liu, B. and Gao, C., 2023. Multiscale modeling of woven composites by deep learning neural networks and its application in design optimization. Composite Structures, p.117553. DOI: 10.1016/j.compstruct.2023.117553
  4. Liu, B. and Liu, X.*, 2025. Neural network-assisted design optimization with adaptive sampling for tow-steered composite structures. Composite Structures, 373(1), p.119588. DOI: 10.1016/j.compstruct.2025.119588
  5. Tao, F.*, Liu, X., Du, H., Tian, S. and Yu, W., 2022. Discover failure criteria of composites from experimental data by sparse regression. Composites Part B: Engineering, 239, p.109947. DOI: 10.1016/j.compositesb.2022.109947
  6. Zhang, L.*, Liu, X., Tian, S. Gao, Z., Haynes, R. Yu, W., 2025. Machine learning-aided cohesive zone modeling of fatigue delamination. Mechanics of Advanced Materials and Structures. (to appear)
  7. Liu, X.*, Kan, C. and Ye, Z., 2022. Real-time multiscale prediction of structural performance in material extrusion additive manufacturing. Additive Manufacturing, 49, p.102503. DOI: doi.org/10.1016/j.addma.2021.102503
  8. Yang, Y., Kan, C.-, and Liu, X., 2022 Point cloud based online detection of geometric defects for the certification of additively manufactured mechanical metamaterials, Journal of Manufacturing Systems, 65, p. 591-604. DOI: 10.1016/j.jmsy.2022.09.011
  9. Ye, Z., Liu, X., Peng, B., and Kan, C.*, 2024, Predicting Mechanical Behavior of Additively Manufactured Mechanical Metamaterials using Point Cloud Representation Learning, Journal of Computing and Information Science in Engineering, 24, 060901-1. DOI: 10.1115/1.4064147