Acta Mechanica

, Volume 230, Issue 3, pp 1061–1076 | Cite as

First-order perturbation-based stochastic homogenization method applied to microscopic damage prediction for composite materials

  • Tien-Dat HoangEmail author
  • Naoki Takano
Original Paper


In this paper, a first-order perturbation-based stochastic homogenization method was developed to predict the probabilities of not only macroscopic properties but also microscopic strain damage in multiphase composite materials, considering many random physical parameters. From the stochastic solution of microscopic strains, damage propagation was analyzed to predict where progressive damage would occur in the microstructures of composites subject to a given macroscopic strain. As an example, a short fiber-reinforced plastic, consisting of short fibers, matrix, and interphase, was used to show the influence of random physical parameters for each constituent material on the variability of the homogenized properties and microscopic strain. In another example, a coated particle-embedded composite material was stochastically analyzed to consider even slight influences of uncertainty in the mechanical properties of the coating material and show damage propagation in this coating layer. Characteristic displacements representing material heterogeneity were thoroughly investigated and extensively used with the aim of reducing the computational cost of finding them in a nonlinear analysis of the microscopic damage propagation.


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This work was supported by a Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (B) (KAKENHI Grant No. 16H04239). The first author thanks the Ministry of Education, Culture, Sports, Science, and Technology of Japan for support in the form of a full scholarship to study and research at Keio University.


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© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Faculty of International TrainingThai Nguyen University of TechnologyTich Luong DistrictVietnam
  3. 3.Department of Mechanical EngineeringKeio UniversityYokohamaJapan

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