dear all

i am trying to implement needleman's polynomial traction separation law in VUMAT explicit subroutine of ABAQUS. I have learnt that it can be only done by defining the tangent or secent stiffness.

however, i don't have much idea regarding both the stiffness. Will anyone please elaborate?

earlier, i have defined the stiffness as a derivative of traction across the fracture surface. The simulation shows negative dilation error due to bad material data. how to rectify that ?

thanks in advance.