Analytical solution for double cantilever beam based on cohesive zone model considering shear deformation

The analytical method can not only solve the deflection of double cantilever beam (DCB) specimens based on cohesive zone model (CZM), but also inversely solve the cohesive constitutive parameters through using only the experimental load displacement data. Where, the governing equation of the Euler-Bernoulli beam based on elastic foundation model (EB-EF) was usually used. Because the governing equation of the Timoshenko beam based on elastic foundation model (EBEF) is difficult to be applied directly to CZM with the nonlinear constitutive relations. To tackle this problem, a new governing equation of the Timoshenko Beam based on Cohesive Zone Model (TB-CZM) is derived in this work and it is suitable for any traction-separation relations. The validity of the derived analytical solutions is verified by numerical CZM results. The effect of shear deformation is studied within the range of material properties and geometric dimensions in the literature. Furthermore, the cohesive parameters are obtained by inversely solving the derived governing equation. Valid cohesive parameters can be obtained by using the proposed method when the input parameters exist some degrees of uncertainty.