PSI - Issue 33

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Derouiche Sami et al. / Procedia Structural Integrity 33 (2021) 996–1006 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Nomenclature a Crack length [B] The strain-displacement transformation matrix E ij Young modulus G ij Shear modulus G Energy release rate [K] Stiffness matrix [M] The matrix of interpolation functions for stresses [N] The matrix of interpolation functions for displacements q Nodal displacement u Displacement node ν ij Poisson’s ratio π ij The deformation energy of the cracked structure ξ, η Coordinates of the natural plan σ Stress τ Shear stress

1. Introduction For a cracked solid submitted to a load that causes its expansion, this expansion does not strictly grow in a straight direction but can deflect in any new path. The common factors that influence manly the crack kinking are the nature of the solid contained in the body, its geometric form, and the imposed loading/deformation on that body. Besides analytics solutions for this phenomenon, there are numerical approaches that can foresee what will occur in the solid. Many recent types of research have given interest to the study of the crack behavior on orthotropic bodies. Fallah and Nikraftar (2018) developed a meshless infinite volume formulation to analyze fracture problems in orthotropic media; the numerical results are compared to previous works (Hybrid-displacement, conservative law of elasticity, FEM-modified crack closure, and FEM-displacement correlation technique, XFEM) proving the accuracy of the formulation. Ma et al. (2007) investigated the crack problem for mode I and mode II on an orthotropic FGM under time-harmonic loading Dag, Yildirim, and Sarikaya (2007)also studied the same problem but took into account both mechanical and thermal loads. While Afshar, Hatefi Ardakani, and Mohammadi (2016) used a crack tip enrichment function to analyze the problem of a crack in an orthotropic bi-material under dynamic loading. Monfared and Ayatollahi (2016) developed an analytical method to study the mode I & II conduct of functionally graded orthotropic plane containing multiple cracks, Sadowski et al. (2016) investigated mode I three collinear cracks in an orthotropic media with normal uniform stress while Zhao et al. (2013) studied periodic parallel cracks in orthotropic bodies under uniformly distributed loads. Pant, Singh, and Mishra (2013) exhibited a new enrichment system for modeling kinking cracks using the EFG technique and analyzed. Tafreshi (2017) propose a new analytic method of J 2 -integral for analyzing a crack between two orthotropic materials.