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3 results

  • 1 - Introduction

  • Leiting Dong, Beihang University, China, Satya N. Atluri, University of California, Irvine
  • Book:
    Computational Grains
    Published online:
    05 October 2023
    Print publication:
    19 October 2023, pp 1-16
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  • Summary

    This chapter provides a very brief summary of the types of heterogeneous materials considered in this monograph: fiber-reinforced composites, particulate composites, nanocomposites, porous composites, and so on. A succinct summary is given of analytical homogenization methods to determine the overall properties of particulate composites based on the upper and lower bounds of Hashin and Shtrikman; the Eshelby ellipsoidal inclusion theory and the Self-consistent Method of Eshelby; and the Mori-Tanaka Method and some other semi-analytical methods. Numerical methods such as the finite element method, the boundary element method, XFEM, and so on to model a representative volume element (RVE) of a heterogeneous material are reviewed, and thus the motivation for the Computational Grains method discussed in the rest of this book is presented.

Computational Grains
  • Micromechanical Genome for Heterogeneous Materials
  • Leiting Dong, Satya N. Atluri
  • Published online:
    05 October 2023
    Print publication:
    19 October 2023
  • This is the first book that systemically introduces the theory and implementation of Computational Grains for micromechanical modeling of heterogeneous materials. This book covers the specifically designed mathematics embedded in Computational Grains, and the entire process of microstructure construction, tessellation, CG simulation and homogenization. The Computational Grains discussed in this book consider elastic, non-elastic, and multi-physics solids. Materials damage development are also preliminarily discussed, with CGs considering matrix-inclusion debonding as well as embedded microcracks. Presenting the theory step-by-step and with detailed examples and MATLAB codes, the material is accessible and practical for readers. This will be ideal for graduate students and researchers in mechanical and aerospace engineering and applied mechanics.