A variational model for stress analysis in cracked laminates with arbitrary symmetric lay-up under general in-plane loading

A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates

“…The reader is referred to Ref. [15] to find details about solving these differential equations. Moreover, it is noted that the coupled system in Equations (21) and (22) is very similar to the equations which has been derived by McCartney [23] using a stress transfer model for general symmetric laminates containing ply cracks.…”

“…Contrary to displacement-based approaches, the approximate stress field derived with variational approaches satisfy exactly all the necessary equilibrium equations, interlaminar continuity and boundary conditions including zero-stress conditions at the free edges as well as the top and bottom surfaces of laminates. This approach was first introduced by Hashin [14] in 1985 for the analysis of cracked two-layer cross-ply laminates under uniaxial tension and further developed by many authors for analyzing cracked laminates with general lay-ups, see for example [15][16][17][18] as the most complete variational models developed so far. Kassapoglou and Lagace [10,19] were the first who applied the variational approach for analyzing stress concentrations near free edges.…”

“…Therefore, the interlaminar stress transfer problem can be reduced to a simple boundary value problem which is dependent only on the axial or transverse coordinate of the assumed laminate. For the variational free-edge stress transfer analysis [10,19] unlike the developed variational ply cracking models [15][16][17][18], this boundary value problem leads to a set of non-homogeneous differential equations as the Euler's equation(s) from the variational calculus.…”

Predicting Properties of Undamaged and Damaged Carbon Fibre Reinforced Composites

“…Only the values of the thermo-elastic constants are affected by the damage. It should be noted that recently Hajikazemi and Sadr [41] have developed a variational method of estimating the effective thermo-elastic constants of general symmetric laminates.…”

Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

“…In laminated composite plates the presence of delaminations and cracks reduces the strength and stiffness (e.g. [14,15]) and changes the dynamic properties significantly, and therefore has a major influence on the lifetime of the structure. The delamination behavior of composite materials is characterized by different specimens for mode-I [16][17][18][19][20][21][22][23], mode-II [24][25][26], mixed-mode I/II [27][28][29][30][31][32][33][34][35][36][37], mode-III [38][39][40][41][42][43][44][45][46][47][48], mixed-mode I/III [49] mixed-mode II/III [42,[50][51][52][53][54][55][56][57][58][59] and mixed-mode I/II/III [60]...…”