An open frontier in mechanical science is the efficient and accurate description of heterogeneous material behavior that strongly depends on complex microstructure. We will explore this using mechanistic data-science multiscale finite element and numerical methods for material homogenization and concurrent multiscale analysis and design. Self-Consistent Clustering Analysis (SCA) concurrent homogenization was developed to directly generating material laws on-the-fly, using an efficient two-stage solution to compute microscale material response from a statistically Representative Volume Element (RVE). The first stage, known as the offline or training stage, uses data science theories such as k-means clustering and self-organizing maps to “compress” the RVE. Next, the “prediction” stage solves the Lippmann-Schwinger equation to determine the response of each compressed RVE (CRVE) to arbitrary applied load with any constitutive relationship. The CRVE may then be considered a material point in the larger concurrent simulation.  The SCA theory integrates multiscale mechanics of materials and data science theories to efficiently generate accurate material laws with a drastic reduction of computational cost over conventional approaches. Prediction comparisons with direct numerical simulations and limited experiments of nonlinear behavior for metal alloys, nano-polymer composites, and polymer matrix composites are given. These use different constitutive laws within the CRVEs; in each case, computational expense is decreased substantially. Applications of data science methods and SCA to nonlinear behavior of advanced and additive manufacturing and jointing technologies will also be discussed.

Liu, Z., Bessa, M.A., Liu, W.K., "Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials." CMAME 306 (2016): 319-341.

Liu, Z., Moore, J.A., Liu, W.K., “An Extended Micromechanics Method for Probing Interphase Properties in Polymer Nanocomposites,” Journal of the Mechanics and Physics of Solids, 95, 663-680, 2016.

Liu, Z., Fleming, M., Liu, W.K., "Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials." CMAME 330 (2018): 547-577.

Bessa, M. A., et al. "A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality." CMAME 320 (2017): 633-667.

Liu, Z., et al, "Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity." In Advances in Computational Plasticity, pp. 221-242. Springer, Cham, 2018.

Tang, S., Zhang, L., Liu, W.K., “From Virtual Clustering Analysis to Self-consistent Clustering Analysis: A Mathematical Study.” Computational mechanics, (2018). https://doi.org/10.1007/s00466-018-1573-x.

Professor Wing Kam Liu is the Walter P. Murphy Professor of Northwestern University, Director of Global Center on Advanced Material Systems and Simulation, President of the International Association for Computational Mechanics (IACM), Past Chair (2017-2018) (Chair 2015-2016) of the US National Committee on TAM and Member of Board of International Scientific Organizations, both within the US National Academies. Selected synergistic activities includes the development of ICME multiscale theories, methods, and software with experimental validations for the design and analysis of engineering material systems, materials design, advanced and additive manufacturing; and technology transfer.  He has over 37 years of engineering and manufacturing consulting, including a broad array of companies and industries, small businesses, and international corporations. Liu’s selected honors include Japan Society of Computational Engineering Sciences Grand Prize; Computational Mechanics Award from Japanese Society of Mechanical Engineers; Honorary Professorship from Dalian University of Technology, IACM Gauss-Newton Medal (highest honor) and Computational Mechanics Award; ASME Dedicated Service Award, ASME Robert Henry Thurston Lecture Award, ASME Gustus L. Larson Memorial Award, ASME Pi Tau Sigma Gold Medal and ASME Melville Medal; John von Neumann Medal (highest honor) and Computational Structural Mechanics Award from the US Association of Computational Mechanics (USACM). He was the founding Director of the NSF Summer Institute on Nano Mechanics and Materials and Founding Chair of the ASME NanoEngineering Council. He is the editor of two International Journals and honorary editor of two journals and has been a consultant for more than 20 organizations. Liu has written four books; and he is a Fellow of ASME, ASCE, USACM, AAM, and IACM.

Li, Y, Abberton BC, Kroger M. Liu WK, Challenges in Multiscale Modeling of Polymer Dynamics, Polymers, June, 2013, 5(2), 751-852. (The most cited article in the past 36 months)    

Ying Li, Martin Kröger, Wing Kam Liu, Endocytosis of PEGylated nanoparticles accompanied by structural and free energy changes of the grafted polyethylene glycol, Biomaterials, 35 (2014) 8467-8478, DOI: 10.1016/j. Biomaterials.2014.06.032.  (More than 4,700 downloads from July 2014 to June 2015)    

Wentao Yan, Wenjun Ge, Jacob Smith, Stephen Lin, Orion L Kafka, Feng Lin, Wing Kam Liu, “Multi-scale Modeling of Electron Beam Melting of Functionally Graded Materials,” Acta Materialia, 2016.