Cubic Traction Law

The Traction Law

This traction law assumes use a cubic function for traction as a function of crack opending displacement (COD). This cubic relation is choosen such that the slope is zero at δ_c and the peak always occurs at δ_c. This traction law was first proposed by Needleman. It has a convenient smooth shape for numerical calculations and the zero slope at δ_c may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is

      [math]\displaystyle{ \sigma = {27\over 4}\sigma_{max} {\delta\over\delta_c}\left(1-{\delta\over\delta_c}\right)^2 }[/math] . There are separate traction laws for opening displacement (mode I) and sliding displacement (mode II).

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