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This book presents an analytical framework for calculating the fracture toughness of generally layered beam structures with an elastically coupled response and hygrothermal stresses. The beam under study features several peculiarities: it consists of multiple layers of dissimilar materials, features bending-extension coupling, and contains residual hygrothermal stresses. Here, a generic analytical model is proposed to compute the energy release rate and the mode mixity. Mechanics of composite materials, crack closure integral, and energetic methods are among the theoretical tools employed for developing the model.A wealth of new closed-form expressions is presented, together with their validation through finite element analyses, which enables investigating various material systems and testing configurations. Experimentalists will find directions for the design and interpretation of delamination tests on laminated composites with uncommon stacking sequences. At the same time, theoreticians can exploit the analytical solution as a benchmark test for more refined analytical and numerical models.