Exponential Traction Law

This traction law assumes the triangular shape for traction as a function of crack opending displacement (COD) during uniaxial, monotonic loading. There are separate and uncoupled traction laws for opening displacement (mode I) and sliding displacement (mode II).

The toughness of this traction law is the area under the curve or:

      [math]\displaystyle{ J_c = {1\over 2} \sigma\delta_c }[/math]

When creating this traction law, you have to enter exactly two of these three properties for both mode I and mode II (i.e., two of J_Ic, σ_I, and δ_Ic and two of J_IIc, σ_II, and δ_IIc). Whichever property is not specified will be calculated from the two provided properties using one of the following relations:

      [math]\displaystyle{ \delta_c = {2J_c\over \sigma}, \qquad \sigma = {2J_c\over \delta_c}, \qquad {\rm or} \qquad J_c = {1\over 2}\sigma\delta_c }[/math]