Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials

Zeliang Liu, Mark Fleming, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Multiscale modeling of heterogeneous material undergoing strain softening poses computational challenges for localization of the microstructure, material instability in the macrostructure, and the computational requirement for accurate and efficient concurrent calculation. In the paper, a stable micro-damage homogenization algorithm is presented which removes the material instability issues in the microstructure with representative volume elements (RVE) that are not sensitive to size when computing the homogenized stress–strain response. The proposed concurrent simulation framework allows the computation of the macroscopic response to explicitly consider the behavior of the separate constituents (material phases), as well as the complex microstructural morphology. A non-local material length parameter is introduced in the macroscale model, which will control the width of the damage bands and prevent material instability. The self-consistent clustering analysis (SCA) recently proposed by Liu et al. [1] provides an effective way of developing a microstructural database based on a clustering algorithm and the Lippmann–Schwinger integral equation, which enables an efficient and accurate prediction of nonlinear material response. The self-consistent clustering analysis is further generalized to consider complex loading paths through the projection of the effective stiffness tensor. In the concurrent simulation, the predicted macroscale strain localization is observed to be sensitive to the combination of microscale constituents, showing the unique capability of the SCA microstructural database for complex material simulations.

Original languageEnglish (US)
Pages (from-to)547-577
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Mar 1 2018


  • Concurrent simulation
  • Data compression in model reduction
  • Microstructural database
  • Multi-scale damage models
  • Non-local damage model
  • Self-consistent scheme

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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