Lee et al. (2010) — Prediction of ECC Tensile Stress-Strain Curves
Citation
Bang Yeon Lee, Jin-Keun Kim, Yun Yong Kim (2010). Prediction of ECC tensile stress-strain curves based on modified fiber bridging relations considering fiber distribution characteristics. Computers and Concrete, 7(5), 455–468.
- DOI:
10.12989/cac.2010.7.5.455 - Atlas layer: supporting
- Related Victor Li book chapter: Chapter 4: Micromechanics-Based Material Design (also Chapter 6)
- Source PDF:
primary_data/lee-2010-prediction-of-ecc-tensile-stress-strain.pdfIJP00510E_Prediction of ECC_CAC.pdf` - Extracted text:
secondary_data/full_texts/lee-2010-prediction-of-ecc-tensile-stress-strain_full_text.mdsecondary_data/full_texts/IJP00510E_Prediction of ECC_CAC_full_text.md` - Source note:
secondary_data/source_notes/lee-2010-prediction-of-ecc-tensile-stress-strain_source_note.mdsecondary_data/source_notes/IJP00510E_Prediction of ECC_CAC_source_note.md`
Why this paper matters
Establishes a complete computational framework connecting micro-scale fiber-bridging laws ($\sigma-\delta$) with macro-scale tensile stress-strain ($\sigma-\epsilon$) response in ECC by deriving an analytical crack spacing equation that explicitly accounts for sectional fiber distribution.
Main contribution
- Analytical Crack Spacing Equation: Formulated a closed-form crack spacing equation ($x'\theta$) for short random fibers accounting for frictional build-up ($F$).}$), pulley force ($F_{pul}$), snubbing correction ($\alpha_s = 0.81$), and fiber count coefficient ($\alpha_{nf
- Multi-Linear Bridging Model: Simplified non-linear $\sigma-\delta$ curves into energy-equivalent multi-linear branches suitable for structural numerical analysis.
- Stochastic Tensile Simulation: Replicated experimental sawtooth stress drops, multiple micro-cracking, and ultimate strain capacity under 95 % normal distribution confidence bounds.
Evidence summary
- Calculated Crack Spacing: Calculated $x'_\theta = 1.39\text{ mm}$ (
wc60wos), $1.47\text{ mm}$ (wc60ws), $1.54\text{ mm}(wc48wos), $1.81\text{ mm}(wc48ws) (Table 7, Page 466). - Peak Bridging Parameters: Peak bridging stress $\sigma_0 = 4.74 \sim 5.85\text{ MPa}$ at crack openings $\delta_0 = 49.0 \sim 64.3\ \mu\text{m}$ (Table 6, Page 465).
- Tensile Response Agreement: High fidelity in predicting first cracking strength ($3.41 \sim 5.20\text{ MPa}$) and multiple cracking strain-hardening plateau (Fig. 8, Page 466).
Linked Atlas nodes
02_concepts/fiber_bridging_law.md02_concepts/strain_hardening_criteria.md05_experiments/crack_width_distribution.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 and Chapter 6 by providing an explicit analytical link between micromechanical fiber parameters and macroscopic finite-element tensile modeling.
Claim-evidence rows to add
| Atlas node | Claim | Evidence summary | Page/Figure/Table | Status |
|---|---|---|---|---|
05_experiments/crack_width_distribution.md |
Crack spacing increases with matrix tensile strength and is governed by frictional stress transfer | Derived crack spacing Eq. (15) predicts $x'_\theta = 1.39 - 1.81\text{ mm}$ across varying matrix strengths | Page 455 & 466 / Eq. (15) / Table 7 | verified_from_pdf |
02_concepts/fiber_bridging_law.md |
Measured fiber orientation yields larger crack opening at peak bridging stress ($\delta_0 = 49-64\ \mu\text{m}$) than 2D/3D models | Measured $p(\theta)$ model predicted $\delta_0 = 64.3\ \mu\text{m}$ for wc60ws vs 45 $\mu\text{m}$ (2D) and 36 $\mu\text{m}$ (3D) |
Page 465 / Table 6 / Fig. 7 | verified_from_pdf |
05_experiments/direct_tensile_test.md |
Multi-linear stochastic bridging simulation captures sawtooth multiple cracking in uniaxial tension | Simulated $\sigma-\epsilon$ curves agree with experimental curves from Kim et al. (2007) | Page 466 / Fig. 8 | verified_from_pdf |
Verification status
- PDF preserved: yes (in
primary_data/IJP00510E_Prediction of ECC_CAC.pdf) - Text extracted: yes (PyMuPDF, 14 pages)
- DOI verified: yes (
10.12989/cac.2010.7.5.455) - Page/figure/table verified: yes (all checked in PDF text)
- Claim-evidence matrix ready: yes
Cautions
- 1D bar element formulation simulates uniaxial tension only; shear and multi-axial stress states require 2D/3D continuum extension.