Spherical inclusion with time-harmonic eigenfields in strain gradient elasticity considering the effect of micro inertia

Askes, 2011, Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48, 1962, 10.1016/j.ijsolstr.2011.03.006 Bennett, 2007, Elasticity theories with higher-order gradients of inertia and stiffness for the modelling of wave dispersion in laminates, Int. J. Fract., 148, 185, 10.1007/s10704-008-9192-8 Delfani, 2017, Overall properties of particulate composites with periodic microstructure in second strain gradient theory of elasticity, Mech. Mater., 113, 89, 10.1016/j.mechmat.2017.07.013 Delfani, 2017, Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity, Proc. R. Soc. Lond. A, 20170254 Eshelby, 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. A, 241, 376, 10.1098/rspa.1957.0133 Eshelby, 1959, The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. Lond. A, 252, 561, 10.1098/rspa.1959.0173 Eshelby, 1961, Elastic inclusions and inhomogeneities, 87 Fafalis, 2012, On the capability of generalized continuum theories to capture dispersion characteristics at the atomic scale, Eur. J. Mech. A Solids, 36, 25, 10.1016/j.euromechsol.2012.02.004 Fu, 1983, The determination of the elastodynamic fields of an ellipsoidal inhomogeneity, J. Appl. Mech., 50, 390, 10.1115/1.3167050 Gao, 2009, Green’s function and Eshelby’s tensor based on a simplified strain gradient elasticity theory, Acta Mech., 207, 163, 10.1007/s00707-008-0109-4 Gao, 2010, Solution of Eshelby’s inclusion problem with a bounded domain and Eshelby’s tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory, J. Mech. Phys. Solids, 58, 779, 10.1016/j.jmps.2010.01.006 Gao, 2010, Strain gradient solution for Eshelby’s ellipsoidal inclusion problem, Proc. R. Soc. Lond. A, 20090631 Georgiadis, 2000, Torsional surface waves in a gradient-elastic half-space, Wave Motion, 31, 333, 10.1016/S0165-2125(99)00035-9 Georgiadis, 2004, Dispersive rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity, J. Elast., 74, 17, 10.1023/B:ELAS.0000026094.95688.c5 Gourgiotis, 2015, Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin–Mindlin gradient theory, Int. J. Solids Struct., 62, 217, 10.1016/j.ijsolstr.2015.02.032 Gourgiotis, 2013, On the reflection of waves in half-spaces of microstructured materials governed by dipolar gradient elasticity, Wave Motion, 50, 437, 10.1016/j.wavemoti.2012.10.004 Markenscoff, 2016, On the dynamic generalization of the anisotropic Eshelby ellipsoidal inclusion and the dynamically expanding inhomogeneities with transformation strain, J. Micromech. Mol. Phys., 1, 1640001, 10.1142/S2424913016400014 Markenscoff, 2010, The energy-release rate and “self-force” of dynamically expanding spherical and plane inclusion boundaries with dilatational eigenstrain, J. Mech. Phys. Solids, 58, 1, 10.1016/j.jmps.2009.10.001 Michelitsch, 2003, Dynamic Eshelby tensor and potentials for ellipsoidal inclusions, Proc. R. Soc. Lond. A, 459, 863, 10.1098/rspa.2002.1054 Michelitsch, 2005, On the retarded potentials of inhomogeneous ellipsoids and sources of arbitrary shapes in the three-dimensional infinite space, Int. J. Solids Struct., 42, 51, 10.1016/j.ijsolstr.2004.07.022 Mikata, 1990, Elastic field due to a dynamically transforming spherical inclusion, J. Appl. Mech., 57, 845, 10.1115/1.2897650 Mindlin, 1964, Micro-structure in linear elasticity, Arch. Ration. Mech. Anal., 16, 51, 10.1007/BF00248490 Mindlin, 1965, Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Struct., 1, 417, 10.1016/0020-7683(65)90006-5 Mindlin, 1968, On first strain-gradient theories in linear elasticity, Int. J. Solids Struct., 4, 109, 10.1016/0020-7683(68)90036-X Ni, 2015, On self-similarly expanding Eshelby inclusions: spherical inclusion with dilatational eigenstrain, Mech. Mater., 90, 30, 10.1016/j.mechmat.2015.02.003 Ni, 2016, The dynamic generalization of the Eshelby inclusion problem and its static limit, Proc. R. Soc. Lond. A, 472, 20160256 Ni, 2016, The self-similarly expanding Eshelby ellipsoidal inclusion: I. Field solution, J. Mech. Phys. Solids, 96, 683, 10.1016/j.jmps.2016.02.025 Ni, 2016, The self-similarly expanding Eshelby ellipsoidal inclusion: II. The dynamic Eshelby tensor for the expanding sphere, J. Mech. Phys. Solids, 96, 696, 10.1016/j.jmps.2016.02.023 Papargyri-Beskou, 2008, Static, stability and dynamic analysis of gradient elastic flexural kirchhoff plates, Arch. Appl. Mech., 78, 625, 10.1007/s00419-007-0166-5 Papargyri-Beskou, 2009, Wave dispersion in gradient elastic solids and structures: a unified treatment, Int. J. Solids Struct., 46, 3751, 10.1016/j.ijsolstr.2009.05.002 Papargyri-Beskou, 2012, Wave propagation in and free vibrations of gradient elastic circular cylindrical shells, Acta Mech., 223, 1789, 10.1007/s00707-012-0643-y Polizzotto, 2012, A gradient elasticity theory for second-grade materials and higher order inertia, Int. J. Solids Struct., 49, 2121, 10.1016/j.ijsolstr.2012.04.019 Polyzos, 2003, A boundary element method for solving 2-d and 3-d static gradient elastic problems: part I: integral formulation, Comput. Methods Appl. Mech. Eng., 192, 2845, 10.1016/S0045-7825(03)00289-5 Sarvestani, 2008, Determination of the scattered fields of an SH-wave by an eccentric coating-fiber ensemble using DEIM, Int. J. Eng. Sci., 46, 1136, 10.1016/j.ijengsci.2008.05.001 Shodja, 2009, 3D elastodynamic fields of non-uniformly coated obstacles: notion of eigenstress and eigenbody-force fields, Mech. Mater., 41, 989, 10.1016/j.mechmat.2009.05.005 Shodja, 2015, Scattering of an anti-plane shear wave by an embedded cylindrical micro-/nano-fiber within couple stress theory with micro inertia, Int. J. Solids Struct., 58, 73, 10.1016/j.ijsolstr.2014.12.020 Toupin, 1962, Elastic materials with couple-stresses, Arch. Ration. Mech. Anal., 11, 385, 10.1007/BF00253945 Vavva, 2009, Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone, J. Acoust. Soc. Am., 125, 3414, 10.1121/1.3110203 Wang, 2005, On the solution of the dynamic Eshelby problem for inclusions of various shapes, Int. J. Solids Struct., 42, 353, 10.1016/j.ijsolstr.2004.06.042 Willis, 1965, Dislocations and inclusions, J. Mech. Phys. Solids, 13, 377, 10.1016/0022-5096(65)90038-4 Xu, 2016, Closed-form frequency solutions for simplified strain gradient beams with higher-order inertia, Eur. J. Mech. A Solids, 56, 59, 10.1016/j.euromechsol.2015.10.005 Zhang, 2005, Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems, Int. J. Solids Struct., 42, 3833, 10.1016/j.ijsolstr.2004.12.005