The three fracture modes (classical classification)

In fracture mechanics, cracks are classified into three fundamental modes:

• Mode I → Opening (tensile)

• Mode II → Sliding (in-plane shear)

• Mode III → Tearing (anti-plane shear)

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Key classification: in-plane vs anti-plane

In-plane modes (Modes I & II)

These involve motion within the crack plane

🔸 Mode I (Opening mode)

• Displacement normal to the crack surface, but still within the 2D plane

• Think: crack faces pull apart

🔸 Mode II (Sliding mode)

• Displacement parallel to the crack front

• Shear motion within the plane

👉 Both are in-plane because:

• Motion is fully described by (u_x, u_y)

• No out-of-plane component

Anti-plane mode (Mode III)

🔸 Mode III (Tearing mode)

• Displacement is perpendicular to the plane

• Crack surfaces slide out of the page

👉 This is anti-plane because:

• Motion is entirely in (z)-direction

• Decoupled scalar problem (SH wave)

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Clean summary table

Fracture Mode	Physical Meaning	Plane Category	Displacement
Mode I	Opening (tension)	in-plane	(u_x, u_y)
Mode II	Sliding (shear)	In-plane	(u_x, u_y)
Mode III	Tearing (shear)	Anti-plane	(u_z)

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Why this classification matters (deep insight)

This is not just naming—it reflects fundamental physics:

🔸 In-plane (Modes I & II)

• Governed by coupled Navier equations

• Generates:

  • P waves (compression)

  • SV waves (in-plane shear)

• More complex:

  • dilation + shear coupling

  • important for real earthquakes

🔸 Anti-plane (Mode III)

• Governed by scalar wave equation

• Generates:

  • SH waves only

• Much simpler:

  • no volumetric strain

  • no coupling