Book contents
- Computational Grains
- Computational Grains
- Copyright page
- Contents
- Preface
- 1 Introduction
- 2 Computational Homogenization in the Micromechanics of Heterogeneous Materials
- 3 Direct Numerical Simulation of Materials Using Computational Grains
- 4 Trefftz Trial Functions for Computational Grains for Planar and 3D Problems
- 5 Computational Grains for Particulate Composites and Porous Materials
- 6 Computational Grains for Cylindrical Fiber Composites
- 7 Computational Grains for Nanocomposites
- 8 Computational Grains for Composites with Coated Inclusions
- 9 Computational Grains for Viscoelastic Composites
- 10 Computational Grains for Piezoelectric Composites/Porous Materials
- 11 Computational Grains with Embedded Microcracks in the Matrix and Inclusions
- 12 Multi-Scale Modeling of Composite Structures Using Computational Grains
- Index
- References
2 - Computational Homogenization in the Micromechanics of Heterogeneous Materials
Published online by Cambridge University Press: 05 October 2023
Book contents
- Computational Grains
- Computational Grains
- Copyright page
- Contents
- Preface
- 1 Introduction
- 2 Computational Homogenization in the Micromechanics of Heterogeneous Materials
- 3 Direct Numerical Simulation of Materials Using Computational Grains
- 4 Trefftz Trial Functions for Computational Grains for Planar and 3D Problems
- 5 Computational Grains for Particulate Composites and Porous Materials
- 6 Computational Grains for Cylindrical Fiber Composites
- 7 Computational Grains for Nanocomposites
- 8 Computational Grains for Composites with Coated Inclusions
- 9 Computational Grains for Viscoelastic Composites
- 10 Computational Grains for Piezoelectric Composites/Porous Materials
- 11 Computational Grains with Embedded Microcracks in the Matrix and Inclusions
- 12 Multi-Scale Modeling of Composite Structures Using Computational Grains
- Index
- References
Summary
This chapter discusses the role of a representative volume element (RVE) in the computational homogenization of heterogeneous materials. The use of the finite element method in modeling an RVE is discussed. The role of using the Hill-Mandel boundary conditions, and the use of periodic displacement and aperiodic traction boundary conditions on an RVE are discussed. The advantages of using the present Computational Grains method in modeling an RVE, not only to determine the macro properties of a heterogeneous material but also to determine the detailed interfacial stress states which are damage precursors at the micro level are discussed.
Keywords
- Type
- Chapter
- Information
- Computational GrainsMicromechanical Genome for Heterogeneous Materials, pp. 17 - 26Publisher: Cambridge University PressPrint publication year: 2023
References
Hill, R., “Elastic Properties of Reinforced Solids: Some Theoretical Principles,” Journal of the Mechanics and Physics of Solids, vol. 11, no. 5, pp. 357–372, 1963, https://doi.org/10.1016/0022-5096(63)90036-X.Google Scholar
Mandel, J., “Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique,” in Applied Mechanics, Görtler, H., Ed., 1966: Springer Berlin Heidelberg, pp. 502–509.Google Scholar
Nemat-Nasser, S., Hori, M., and Datta, S. K., “Micromechanics: Overall Properties of Heterogeneous Materials,” Journal of Applied Mechanics, vol. 63, no. 2, p. 561, 1996, https://doi.org/10.1115/1.2788912.CrossRefGoogle Scholar