Trilinear Traction Law

The Traction Law

This traction law assumes a piece-wise linear relation with two arbitrarily-specifiable break points (i.e., three linear pieces). There are separate traction laws for opening displacement (mode I) and sliding displacement (mode II).

The toughness is

      [math]\displaystyle{ J_c = {1\over2}\bigl(\sigma_1\delta_2 + \sigma_2(\delta_2-\delta_1)\bigr) }[/math]

The traction law for each mode depends up seven properties - (δ₁,σ₁) and (δ₂,σ₂) breakpoints, critical COD (δ_c), total area or toughness (J_c), and the initial elastic slope (k). You must enter exactly 5 of these seven properties for each mode. Furthermore, if one of the 5 is the initial slope, then either σ₁ or δ₁ for that mode (but not both) must be one of the five specified properties. The two remaining unspecified parameters will be calculated from the five provided parameters. The final law must satisfy δ₁ ≤ δ₂ ≤ δ_c, δ_c > 0, σ₁ ≥ 0, σ₂ ≥ 0, and σ₁+σ₂ & 0.

Traction Law Properties

The following properties are used to create a triangular traction law:

Property	Description	Units	Default
(other)	Properties common to all traction laws	varies	varies