2012/02/24 by L. Morini, Lorenzo Morini, Morini, Lorenzo +8
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fatigue and fracture mechanics #Mathematical Physics (math-ph) #Numerical methods in engineering #Structural Behavior of Reinforced Concrete #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1202.5418
26 pages, 4 figures
openalex publication_date 2012/02/24 · arxiv created 2012/07/09 · arxiv updated 2012/07/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The focus of the article is on analysis of skew-symmetric weight matrix functions for interfacial cracks in two dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient approach to this challenging task. Conventionally, the weight functions, both symmetric and skew-symmetric, can be identified as a non-trivial singular solutions of the homogeneous boundary value problem for a solid with a crack. For a semi-infinite crack, the problem can be reduced to solving a matrix Wiener-Hopf functional equation. Instead, the Stroh matrix representation of displacements and tractions, combined with a Riemann-Hilbert formulation, is used to obtain an algebraic eigenvalue problem, that is solved in a closed form. The proposed general method is applied to the case of a quasi-static semi-infinite crack propagation between two dissimilar orthotropic media: explicit expressions for the weight matrix functions are evaluated and then used in the computation of complex stress intensity factor corresponding to an asymmetric load acting on the crack faces.