(a) (b) where α is the frictional angle and f$_{c}$ is the compres- sive strength. Furthermore, where β is the ratio of the short and long radii of the cap ellipse (Figure 3). At the point where the two parts of the yield surface meet, the normal stress is σ$_{n0}$ = − a βα √ 1 + β 2 α $_{2}$. The rate of the plastic strains in Equation 2 is where D$_{e}$ is the elastic stiffness, $^{ε}$c = ( ε$_{c}$, 0 , 0) T is the eigenstrain describing the expansion of the corrosion product and $^{ε}$p = ( ε$_{pn}$, ε$_{ps}$, ε$_{pt}$ ) T is the plastic strain. The yield surface of the plasticity model consists of a Mohr-Coulomb friction law combined with an elliptical cap. The shape of the cap surface is adjusted so that a smooth transition between the two surfaces is obtained (Figure 3). This combination was initially proposed by Swan and Seo (2000) and further devel- oped by Dolarevic and Ibrahimbegovic (2007). The yield function f depends on the normal stress σ$_{n}$ and the shear stress norm σ$_{q}$ = √ σ 2 s + σ 2 t as The lattice approach is used to model the experiments reported by Lee et al. (2002). The geometry and load- ing setup of the experiments is shown in Figure 5. Re- inforcement bars ( GLYPH<diameter> = 13 mm) embedded in concrete where λ$_{c}$ is the ratio of the volume ratio of rust and steel. The corrosion penetration x$_{c}$ is related to the corrosion percentage ρ$_{c}$ as The effect of corrosion is idealised as an eigenstrain ε$_{c}$ , which is determined from the free expansion of the corrosion product u$_{c}$ as ε$_{c}$ = u$_{c}$/h (Figure 4). This expansion is related to the corrosion penetration depth x$_{c}$ as 2.2 Model for corrosion between concrete and rein- forcement This plasticity bond model is similar to the one devel- oped by Lundgren (2005a). However, in the present work, the response is assumed to be perfectly plastic, i.e. the shape of the yield surface is independent of the plastic strains. The bond model will be extended to hardening and softening in future work. The imple- mentation of the present model is simplified by intro- ducing a smooth transition between the cap and the frictional law. Thus, a special vertex stress return in the transition region is not required. where g is the plastic potential and λ is the plastic multiplier. In the present study, g is chosen to be very similar to the yield function f . The only difference is that α is replaced by the dilatancy angle ψ so that the magnitude of the normal plasticity strain generated during shear loading can be controlled. The plastic- ity model is completed by the loading and unloading conditions: Figure 2: Interface. (a) Tangential plane of interface with the local coordinate system n , s and t . (b) Cross-section of interface of thickeness h . a = βαf$_{c}$ αβ + √ 1 + β 2 α 2 (4) ˙ $^{ε}$p = ˙ λ ∂g ∂ ¯ σ (5) f ≤ 0 , ˙ λ ≥ 0 , ˙ λf = 0 (6) u$_{c}$ = √ r 2 + (2 rx$_{c}$ − x 2 $_{c}$)( λ$_{c}$ − 1) − r (7) x$_{c}$ = r ( 1 − √ 1 − ρ$_{c}$ 100 ) (8) f =      σ$_{q}$ + ασ$_{n}$ if σ$_{n0}$ ≤ σ$_{n}$ σ 2 $_{q}$+ ( σ$_{n}$ + f$_{c}$ − a ) 2 β 2 − a 2 β 2 if σ$_{n}$ ≤ σ$_{n0}$ (3) Figure 3: Yield surface: Mohr-Coulomb friction law com- bined with a cap. 3 COMPARISON WITH EXPERIMENTAL RE- SULTS