## Fig xA Uncoupled constitutive relationships a normal direction b tangential

Fig. 10. Uncoupled constitutive relationships [14]: (a) normal direction, (b) tangential direction.Figure optionsDownload full-size imageDownload as PowerPoint slide

Since the actual debonding should take both the opening and the sliding modes into account [17], a modified mixed-mode constitutive relationship is presented by Alfano and Crisfield [16]. They set the ratio of relative displacement in the elastic regime to that Cy5 hydrazide in the softening regime to be equal for both the normal and tangential directions.equation(7)η=1-δonδcn=1-δotδct

Then a mixed-mode damage parameter dm could be introduced on the basis of the ratio parameter η.equation(8)dm=max1,1ηΔm∗-1Δm∗where Δm∗ is angina calculated as below,equation(9)Δm∗=max0?τ′?τΔn2(τ′)+Δt2(τ′)=max0?τ′?τ〈δn(τ′)〉δon2+〈δt(τ′)〉δot2

Then the single-mode constitutive relationship (Eq. (4)) can be modified as follows for the mixed-mode delamination,equation(10)tα=φmKαδα=(1-dm)Kαδαtα=φmKαδα=(1-dm)Kαδα