Lee et al. (2010) — Micromechanics-Based Fiber-Bridging Analysis
Citation
B.Y. Lee, Y. Lee, J.K. Kim, Y.Y. Kim (2010). Micromechanics-Based Fiber-Bridging Analysis of Strain-Hardening Cementitious Composite Accounting for Fiber Distribution. CMES: Computer Modeling in Engineering & Sciences, 61(2), 111–132.
- DOI:
10.3970/cmes.2010.061.111 - Atlas layer: supporting
- Related Victor Li book chapter: Chapter 4: Micromechanics-Based Material Design (also Chapter 3)
- Source PDF:
primary_data/lee-2010-micromechanics-based-fiber-bridging-analysis-of-strain-hardening.pdfIJP00410E_Micromechanics based fiber bridging analysis_CMES.pdf` - Extracted text:
secondary_data/full_texts/lee-2010-micromechanics-based-fiber-bridging-analysis-of-strain-hardening_full_text.mdsecondary_data/full_texts/IJP00410E_Micromechanics based fiber bridging analysis_CMES_full_text.md` - Source note:
secondary_data/source_notes/lee-2010-micromechanics-based-fiber-bridging-analysis-of-strain-hardening_source_note.mdsecondary_data/source_notes/IJP00410E_Micromechanics based fiber bridging analysis_CMES_source_note.md`
Why this paper matters
Bridges the gap between theoretical micromechanical models and real experimental tensile behavior in ECC by incorporating image-measured fiber orientation distributions $g(\theta)$ and matrix spalling into the fiber-bridging constitutive law $\sigma_B(\delta)$.
Main contribution
- Realistic Fiber Orientation Integration: Derived an advanced $\sigma_B(\delta)$ bridging equation integrating measured probability density functions $g(\theta)$ and fiber number coefficients $\alpha_{nf}$ from cross-sectional image analysis.
- Matrix Spalling Modeling: Incorporated local matrix chipping ($s$) at inclined fiber exit points, demonstrating how spalling reduces effective inclination and delays premature fiber rupture.
- Accurate Ductility Prediction: Reduced the relative error in predicting experimental ultimate tensile strain ($\epsilon_u$) from > 50-100 % (using 2D/3D random assumptions) down to ~15 % (10.8 % for $w/c=0.60$ ECC).
Evidence summary
- Direct Uniaxial Tensile Performance: Experimental $\epsilon_u = 4.24\text{ \%}$ for slag-added ECC (
wc60ws) and $2.77\text{ \%}$ for control ECC (wc60wos) (Table 5, Page 130). - Prediction Accuracy: Image-based model predicted $\epsilon_u = 3.75\text{ \%}$ for
wc60ws(11.6 % error) and $2.47\text{ \%}$ forwc60wos(10.8 % error) (Table 5, Page 130). - Measured Fiber Density: Real fiber density $F_n = 8.95 \sim 10.6\text{ fibers/mm}^2$ with fiber count coefficient $\alpha_{nf} = 0.708 \sim 0.789$ (Table 4, Page 127).
Linked Atlas nodes
02_concepts/fiber_bridging_law.md02_concepts/strain_hardening_criteria.md02_concepts/interface_properties.md02_concepts/fiber_dispersion.md05_experiments/direct_tensile_test.md
Relationship to Victor Li book
- Primary book anchor remains Victor Li (2019), Engineered Cementitious Composites (ECC).
- Directly supports Chapter 4 (Material Design) and Chapter 3 (Interface & Pullout) by proving that incorporating real non-random fiber orientation distribution resolves discrepancy between theoretical PSH predictions and experimental tensile ductility.
Claim-evidence rows to add
| Atlas node | Claim | Evidence summary | Page/Figure/Table | Status |
|---|---|---|---|---|
02_concepts/fiber_bridging_law.md |
Image-informed fiber orientation distribution $g(\theta)$ predicts ECC tensile ductility within ~15 % error | Measured $\epsilon_u = 4.24\text{ \%}$ predicted as $3.75\text{ \%}$ (11.6 % error) vs > 50 % error under 2D/3D random assumptions | Page 128 / Table 5 / Fig. 10 | verified_from_pdf |
02_concepts/strain_hardening_criteria.md |
GGBS slag addition improves fiber distribution and complementary energy, elevating direct tensile strain capacity to 4.24 % | wc60ws achieved $\epsilon_u = 4.24\text{ \%}$ with stress performance index of 1.43 |
Page 126 & 130 / Table 4 & Table 5 | verified_from_pdf |
02_concepts/interface_properties.md |
Matrix spalling delays fiber rupture by decreasing inclination angle $\theta$ and embedded length $L_e$ | Matrix spalling size $s$ relieves stress concentration and modifies debonding/pullout equilibrium | Page 119 / Eqs. (24)-(32) / Fig. 5 | verified_from_pdf |
Verification status
- PDF preserved: yes (in
primary_data/IJP00410E_Micromechanics based fiber bridging analysis_CMES.pdf) - Text extracted: yes (PyMuPDF, 22 pages)
- DOI verified: yes (
10.3970/cmes.2010.061.111) - Page/figure/table verified: yes (all checked in PDF text)
- Claim-evidence matrix ready: yes
Cautions
- The model's predictive power depends on accurate experimental determination of interfacial bond properties ($\tau_0, G_D, \beta$).
- In high-strength matrices ($w/c=0.48$), elevated matrix fracture toughness causes premature crack localization and loss of strain-hardening ($\epsilon_u < 0.2\text{ \%}$).