Elastodynamics Macro/nano-holes, inclusions, cracks General anisotropy Boundary integral equations Stress concentration factor Stress intensity factor
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 25, No 1, (2015), 155p-166p
The aim of the study is to propose, develop and validate an accurate and efficient boundary integral equation method (BIEM) and apply it for solution of plane dynamic problems for anisotropic composite solids with cracks, inclusions and holes at macro and nano level. The modeling approach is based on the frame of continuum mechanics, linear wave propagation theory, linear fracture mechanics and surface elasticity theory. The computational tool is displacement and non-hypersingular traction BIEM based on frequency dependent fundamental solution. The obtained results reveal the sensitivity of the dynamic stress concentrations fields to the: (a) type of the defect-crack, hole or inclusion; (b) type of the boundary condition at macro or nano scale; (c) characteristics of the dynamic load; (d) material anisotropy; (e) wavedefect, defect-defect interaction. The non-classical boundary conditions and a localized constitutive equation for the matrix-inclusion interfaces within the framework of the Gurtin-Murdoch surface elasticity theory are developed, applied, and reported for the case of isotropic media. The relevant solid matrix could be an infinite or finite-sized medium containing multiple nano-cavities and/or elastic nano-inclusions of arbitrary shape and configuration. 2010 Mathematics Subject Classification: 74J20, 74S15, 74G70.