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Research Papers

Representative Volume Element Based Modeling of Cementitious Materials

[+] Author and Article Information
M. M. Shahzamanian

Department of Mechanical Engineering,
The University of Mississippi,
University, MS 38677

T. Tadepalli

Department of Mechanical Engineering,
The University of Mississippi,
University, MS 38677
e-mail: tadepali@olemiss.edu

A. M. Rajendran

Department of Mechanical Engineering,
The University of Mississippi,
University, MS 38677

W. D. Hodo

U.S. Army Engineer Research
and Development Center,
Vicksburg, MS 39180

R. Mohan

Joint School of Nano Science
and Nano Engineering,
North Carolina A&T State University,
Greensboro, NC 27411

R. Valisetty, P. W. Chung, J. J. Ramsey

U.S. Army Research Laboratory,
Aberdeen Proving Ground, MD

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 26, 2013; final manuscript received October 28, 2013; published online December 9, 2013. Assoc. Editor: Tetsuya Ohashi.

This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Eng. Mater. Technol 136(1), 011007 (Dec 09, 2013) (16 pages) Paper No: MATS-13-1103; doi: 10.1115/1.4025916 History: Received June 26, 2013; Revised October 28, 2013

The current work focuses on evaluation of the effective elastic properties of cementitious materials through a voxel based finite element analysis (FEA) approach. Voxels are generated for a heterogeneous cementitious material (type-I cement) consisting of typical volume fractions of various constituent phases from digital microstructures. The microstructure is modeled as a microscale representative volume element (RVE) in ABAQUS® to generate cubes several tens of microns in dimension and subjected to various prescribed deformation modes to generate the effective elastic tensor of the material. The RVE-calculated elastic properties such as moduli and Poisson's ratio are validated through an asymptotic expansion homogenization (AEH) and compared with rule of mixtures. Both periodic (PBC) and kinematic boundary conditions (KBC) are investigated to determine if the elastic properties are invariant due to boundary conditions. In addition, the method of “Windowing” was used to assess the randomness of the constituents and to validate how the isotropic elastic properties were determined. The average elastic properties obtained from the displacement based FEA of various locally anisotropic microsize cubes extracted from an RVE of size 100 × 100 × 100 μm showed that the overall RVE response was fully isotropic. The effects of domain size, degree of hydration (DOH), kinematic and periodic boundary conditions, domain sampling techniques, local anisotropy, particle size distribution (PSD), and random microstructure on elastic properties are studied.

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Figures

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Fig. 5

Typical volume fractions of major constituents at various stages of curing

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Fig. 4

Schematic diagram of the nanoscale C–S–H particles [17]

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Fig. 3

Work flow of the CEMHYD3D program for generation of cement microstructure

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Fig. 2

Scaled PSD for initial cement powder in domains of various sizes

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Fig. 1

Multilevel microstructure of cement-based materials [2]

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Fig. 10

Schematic showing location of windows extracted from the 1M-PMD

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Fig. 6

(a) 1 K, (b) 8 K, (c) 125 K, and (d) 1M FE models of hydrated cement microstructure (PMDs) (not to scale)

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Fig. 7

200 × 200 × 100 μm (4M) FE model of hydrated cement microstructure (PMD)

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Fig. 8

Prescribed kinematic (KBC) (a) tensile deformation (E1) and (b) pure shear (G12) boundary conditions

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Fig. 13

Variation of (a) principal and (b) shear moduli (KBC) in 1M-PMD for various instances normalized to their respective average

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Fig. 11

Deformation corresponding to pure shear (G12)

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Fig. 12

Volume fractions of major phases for 1 K, 8 K, 125 K, and 1M PMDs

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Fig. 16

The effect of domain size on degree of hydration (α) (CEMHYD3D)

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Fig. 20

Development of the compressive strength (f'c) (CEMHYD3D)

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Fig. 21

Development of the Young's modulus (E) (ABAQUS®)

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Fig. 17

Volume fractions of major phases for (a) 1 K element, (b) 8 K element windows, and (c) 125 K element windows

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Fig. 18

Elastic moduli (uniaxial) with increasing window size

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Fig. 19

Elastic shear moduli Gij with increasing window size

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Fig. 14

Effect of DOH on material bulk properties for 1M-RVE for KBC, PBC, and AEH

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Fig. 15

Effect of domain size on material bulk properties for DOH = 0.8 for KBC, PBC, and AEH

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