In this study two types of non-classical fracture mechanisms are considered, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and fracture of solids under compression along parallel cracks. To investigate non-axisymmetric and axisymmetric problems for infinite solids containing two parallel co-axial cracks or a periodical set of co-axial parallel cracks we use a combined analytical-numerical method in the framework of three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements of the linearized theory via harmonic potential functions. With the use of the integral Fourier – Hankel transformations the problems are reduced to resolving Fredholm integral equations of the second kind. This approach allows to investigate problems in a unified general form for compressible and non-compressible homogeneous isotropic or transversally isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only at the stage of numerical calculation of resolving equations obtained in the general form. The effects of initial stresses on stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversally isotropic elastic bodies). The «resonance-like» effects are found out when compressive initial stresses are reached the values that correspond to the local loss of material stability in the vicinity of the cracks, which, according to the combined method mentioned, allows one to determine critical (limiting) load parameters under compression of the body along the cracks. The conclusions concerning the dependences of stress intensity factors and critical (limiting) parameters of compression on geometrical parameters of the problems are formulated as well as on physical and mechanical characteristics of materials.
