Implementation of Fictitious Crack Model Using Mixed Freedom Finite Element Method

Pairs of contact points were set along the possible developing path of the crack. The Mixed Freedom Finite Element Method proposed for contact problems was extended to implement the mechanics of concrete fracture numerical simulation by the Fictitious Crack Model. The system of forces acting on the structure was divided into two parts: external forces and contact forces. The displacement of structure was chosen as the basic variable and the nodal contact force in possible contact region under local coordinate system was chosen as the iterate variable, so that the nonlinear iteration process was only limited in the possible contact surface and much more economical. Firstly, the basic idea of the Mixed Freedom Finite Element Method was presented. And then, the softening constitutive relation for the concrete was introduced to the method. At last, the validity and accuracy of the proposed procedure was demonstrated by a numerical example.