13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- In the present study the elasto-plastic convex domain is defined by the intersection of the classical Mohr-Coulomb bilinear function with a tension cut-off: ( ) ( ) 1 0 , tan 1 c c c p p p c χ σ φ χ Φ = + − − σ τ (29) ( ) ( ) 2 0 , 1 c c p p p χ σ σ χ Φ = − − σ (30) where c τ and cσ are the tangential stress vector and the normal stress component of the contact stresses, φ is the friction angle, c0 and σ0 the cohesion and tensile strength of the virgin interfaces. The two yield functions are depicted in Fig. 2. The following four zones can be distinguished: I elastic zone: 1 2 0, 0 p p Φ < Φ < II plastic activation in shear: 1 2 0, 0 p p Φ = Φ < III plastic activation in tension: 1 2 0, 0 p p Φ < Φ = IV plastic activation in tension and shear (corner): 1 2 0, 0 p p Φ = Φ = . The damage activation function is linear and the first activation occurs when the thermodynamic force reaches the relative threshold value ζ0: ( ) ( ) 0 , 1 d d d ζ χ ζ ζ χ Φ = − − (31) Figure 2. Plastic yield conditions represented in the stress space. 4. Numerical applications. The interphase model presented in Sections 2 and 3 has been implemented in an open-source research-oriented finite element analysis program for 2D applications. With the aim to run a step-by-step integration, flow rules given in rate form were rewritten as discrete laws. The implicit backward-Euler difference method was applied to obtain results within the time step
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