Calculation of for a multidirectional composite double cantilever beam on two-parametric elastic foundation

In this research, a Timoshenko beam (TB) resting on two-parametric (or Pasternak) elastic foundation (PEF) is developed for determination of strain energy release rate (SERR) of mode-I delamination in multidirectional double cantilever beam (DCB) specimens. Based upon the compliance approach, a closed-form solution is obtained for SERR versus delamination length, applied load, effective mechanical properties, and geometrical dimensions of DCB specimen. The required effective flexural modulus in this model is determined with three different methodologies, plane stress resultant method, plies arrangement method, and using longitudinal tensile and compressive moduli method. The proposed model is assessed by experimental and numerical results available in the literature for various lay-ups. A comprehensive evaluation is also carried out among various theories which are used to model mode-I interlaminar fracture toughness. Results show that the developed model predicts G I at the onset of delamination growth very well for unidirectional and multidirectional DCB specimens. However, the main advantages of this model are: 1) It gives a simple and accurate explicit closed-form solution for SERR of symmetric unidirectional and multidirectional lay-ups in comparison with the high-order shear deformation beam theories with a very lengthy and tedious procedure. 2) It models both first-order transverse shear deformation and local effects at the crack tip (root rotation) to improve the split beam solution. 3) By simplifying the Timoshenko beam on two-parametric foundation, as a generalized case, special cases like Euler–Bernoulli and Timoshenko beams on the Winkler elastic foundation (WEF) are obtainable.