Micromechanics and PSH Criteria

1. Learning objectives

• Explain strength and energy criteria.
• Connect matrix cracking, bridging, and fracture energy.
• Use PSH criteria as a simple design filter.

2. Key concepts

• Strength criterion
• Energy criterion
• Matrix cracking strength
• Complementary energy
• Crack tip toughness
• PSH margin

3. Minimal theory

Pseudo-strain-hardening requires fiber bridging capacity to exceed the matrix cracking demand. Strength margin enables new cracks; energy margin prevents unstable localization.

4. Source-grounded evidence

• Main node: 02_concepts/strain_hardening_criteria.md.
• Related node: 02_concepts/flaw_design.md.
• Evidence matrix: 07_visualization/foundational_papers_claim_evidence_matrix.csv.

5. Representative papers

• Li & Wu 1992.
• Li & Leung 1992.
• Kanda & Li 2006.
• Choi 2020 slag-based composite.

6. Figures/tables to show later

• PSH criteria schematic.
• σ-δ bridging curve.
• Example table of stress and energy performance indices.

7. Discussion questions

1. Why can a stronger matrix reduce ductility?
2. What does flaw design change in the PSH problem?
3. Which is more restrictive: strength or energy criterion?

8. Assignment idea

Given σ0, σfc, Jb, and Jtip, decide if strain-hardening is expected.

9. Linked Atlas nodes

• 02_concepts/strain_hardening_criteria.md
• 02_concepts/flaw_design.md
• 02_concepts/flaw_design.md

10. Suggested reading path

1. 02_concepts/strain_hardening_criteria.md
2. 02_concepts/flaw_design.md
3. 06_lab_position/low_fiber_egc_position.md

Evidence files

• 07_visualization/foundational_papers_claim_evidence_matrix.csv
• 07_visualization/extreme_ductility_extension_claim_evidence_matrix.csv
• 07_visualization/sustainable_ecc_extension_claim_evidence_matrix.csv
• 07_visualization/by_lee_lab_publications_claim_evidence_matrix.csv