Inverse scattering problem of reconstruction of an embedded micro-/nano-size scatterer within couple stress theory with micro inertia

Mechanics of Materials - Tập 103 - Trang 123-134 - 2016
A. Goodarzi1, M. Fotouhi2, H.M. Shodja1,3
1Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
2Department of Mathematics, Sharif University of Technology, Tehran, Iran
3Institute for Nanoscience and Nanotechnology, Sharif University of Technology, Tehran, Iran

Tài liệu tham khảo

Arens, 2009, The linear sampling method revisited, J. Integral Equ. Appl., 2, 179, 10.1216/JIE-2009-21-2-179 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 Cakoni, 2006 Charalambopoulos, 2003, The linear sampling method for non-absorbing penetrable elastic bodies, Inv. Prob., 19, 549, 10.1088/0266-5611/19/3/305 Colton, 1996, A simple method for solving inverse scattering problems in the resonance region, Inv. Prob., 12, 383, 10.1088/0266-5611/12/4/003 Colton, 1997, A simple method using morozovs discrepancy principle for solving the inverse scattering problem, Inv. Prob., 13, 1477, 10.1088/0266-5611/13/6/005 Cosserat, 1909 Eringen, 1968, Theory of micropolar elasticity Erofeyev, 2003 Fata, 2007, Elastic scatterer reconstruction via the adjoint sampling method, SIAM J. Appl. Math., 67, 1330, 10.1137/060653123 Fotouhi, 2007, The singular sources method for cracks, Math. Methods Appl. Sci., 30, 1121, 10.1002/mma.829 Gourgiotis, 2014, Steady-state propagation of a mode II crack in couple stress elasticity, Int. J. Fract., 188, 119, 10.1007/s10704-014-9950-8 Hassen, 2010, The singular sources method for 3D inverse acoustic obstacle scattering problems, SIMA J. Appl. Math., 75, 1 Kirsch, 1998, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inv. Prob., 14, 1489, 10.1088/0266-5611/14/6/009 Mindlin, 1964, Micro-structure in linear elasticity, Arch. Ration. Mech. Anal., 16, 51, 10.1007/BF00248490 Mindlin, 1962, Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11, 415, 10.1007/BF00253946 Mishuris, 2012, Steady-state propagation of a mode III crack in couple stress elastic materials, Int. J. Solids Struct., 61, 112 Morini, 2014, Remarks on the energy release rate for an anti-plane moving crack in couple stress elasticity, Int. J. Solids Struct., 51, 3087, 10.1016/j.ijsolstr.2014.05.005 Morini, 2013, On fracture criteria for dynamic crack propagation in elastic materials with couple stresses, Int. J. Eng. Sci., 71, 45, 10.1016/j.ijengsci.2013.05.005 Philippidis, 2005, Experimental study of wave dispersion and attenuation in concrete, Ultrasonics, 43, 584, 10.1016/j.ultras.2004.12.001 Potthast, 1999 Radi, 2008, On the effects of the characteristic lengths in bending and torsion on mode III crack in couple stress elasticity, Int. J. Solids Struct., 45, 3033, 10.1016/j.ijsolstr.2008.01.010 Savin, 1970, Elastic wave propagation in a solid with microstructure, Sov. Appl. Mech., 6, 725, 10.1007/BF00892125 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 Voigt, 1887, Theoretische studien über die elasticitätsverhältnisse der krystalle, Abh. Ges. Wiss. Göttingen, 34, 3 Yaman, 2013, A survey on inverse problems for applied sciences, Math. Probl. Eng., 2013, 976837