Reflection and transmission of elastic waves at the interface between two distinct micromorphic media are considered in the one-dimensional setting. A dual internal variable approach is used for the description of the microstructure influence on the global motion. It is shown that reflection and transition coefficients for plane waves depend on the coupling between macro- and micro-motions as well as on the choice of the microstructural interaction at the interface. Numerical simulations exhibiting results with promising technological implications are shown.
HirschbergerCBSteinmannP. Modelling of microstructured materials with micromorphic continuum approaches. In Mueller-HoeppeDLoehnertSReeseS (eds) Recent developments and innovative applications in computational mechanics. New York, NY: Springer, 2011, pp. 191–198.
2.
GrilloAFedericoSWittumG. Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials. Int J Non-Lin Mech2012; 47(2): 388–401.
3.
ForestS. Micromorphic media. In AltenbachHEremeyevVA (eds) Generalized continua from the theory to engineering applications. New York, NY: Springer, 2013, pp. 249–300.
4.
AltenbachHEremeyevVA. Direct approach-based analysis of plates composed of functionally graded materials. Arch Appl Mech2008; 78(10): 775–794.
5.
NeffPGhibaIDMadeoA. A unifying perspective: The relaxed linear micromorphic continuum. Continuum Mech Therm2014; 26(5): 639–681.
6.
DingrevilleRRobbinsJVothTE. Wave propagation and dispersion in elasto-plastic microstructured materials. Int J Solid Struct2014; 51(11): 2226–2237.
7.
AchenbachJ. Wave propagation in elastic solids. Amsterdam: Elsevier, 1984.
KellerHB. Propagation of stress discontinuities in inhomogeneous elastic media. SIAM Rev1964; 6: 356–382.
10.
CooperHF. Propagation of one-dimensional waves in inhomogeneous elastic media. SIAM Rev1967; 9: 671–679.
11.
QuiligottiSMauginGAdell’IsolaF. Wave motions in unbounded poroelastic solids infused with compressible fluids. ZAMP2002; 53(6): 1110–1138.
12.
WangYHaoH. Modelling of guided wave propagation with spectral element: Application in structural engineering. Appl Mech Mater2014; 553: 687–692.
13.
HillR. Discontinuity relations in mechanics of solids. Prog Solid Mech1961; 2(72): 245–276.
14.
MorlandLSellersS. Multiphase mixtures and singular surfaces. Int J Non-Lin Mech2001; 36(1): 131–146.
15.
MauginGA. On shock waves and phase-transition fronts in continua. ARI – Int J Phys Eng Sci1998; 50(3): 141–150.
16.
SteinmannPHäsnerO. On material interfaces in thermomechanical solids. Arch Appl Mech2005; 75(1): 31–41.
17.
IrschikH. On rational treatments of the general laws of balance and jump, with emphasis on configurational formulations. Acta Mech2007; 194(1–4): 11–32.
18.
MauginGARousseauM. Wave-quasi-particle dualism in the transmission-reflection problem for elastic waves. J Theor Appl Mech2012; 50: 797–805.
19.
Dell’IsolaFMadeoAPlacidiL. Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua. ZAMM2012; 92(1): 52–71.
20.
PlacidiLRosiGGiorgioI. Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. Math Mech Solid2013; 19(5): 555–578.
21.
EringenAC. Microcontinuum field theories. Volume I. New York, NY: Springer, 1999.
22.
MindlinRD. Micro-structure in linear elasticity. Arch Rat Mech Anal1964; 16: 51–78.
23.
EringenACSuhubiE. Nonlinear theory of simple micro-elastic solids – I. Int J Eng Sci1964; 2(2): 189–203.
24.
CowinSCNunziatoJW. Linear elastic materials with voids. J Elast1983; 13(2): 125–147.
25.
ChenYLeeJDEskandarianA. Atomistic viewpoint of the applicability of microcontinuum theories. Int J Solid Struct2004; 41(8): 2085–2097.
26.
MarangantiRSharmaP. A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies. J Mech Phys Solid2007; 55(9): 1823–1852.
27.
FishJKuznetsovS. From homogenization to generalized continua. Int J Comput Meth Eng Sci Mech2012; 13(2): 77–87.
28.
WangXLeeJD. Micromorphic theory: A gateway to nano world. Int J Smart Nano Mater2010; 1(2): 115–135.
29.
Dell’IsolaFRosaLWoźniakC. A micro-structured continuum modelling compacting fluid-saturated grounds: The effects of pore-size scale parameter. Acta Mech1998; 127(1–4): 165–182.
30.
IeşanD. Method of potentials in elastostatics of solids with double porosity. Int J Eng Sci2015; 88: 118–127.
31.
MadeoAdell’IsolaFDarveF. A continuum model for deformable, second gradient porous media partially saturated with compressible fluids. J Mech Phys Solid2013; 61(11): 2196–2211.
32.
MauginGA. On canonical equations of continuum thermomechanics. Mech Res Commun2006; 33(5): 705–710.
33.
MauginGAMuschikW. Thermodynamics with internal variables Part I. General concepts. J Non-Equil Thermodyn1994; 19(3): 217–249.
34.
MauginGA. Material inhomogeneities in elasticity. Boca Raton, FL: CRC Press, 1993.
35.
MauginGA. On the thermomechanics of continuous media with diffusion and/or weak nonlocality. Arch Appl Mech2006; 75: 723–738.
EngelbrechtJBerezovskiA. Internal structures and internal variables in solids. J Mech Mater Struct2013; 7: 983–996.
41.
BerezovskiAEngelbrechtJMauginGA. One-dimensional microstructure dynamics. In GanghofferJ-FPastroneF (eds) Mechanics of microstructured solids. New York, NY: Springer, 2009, pp. 21–28.
42.
BerezovskiAEngelbrechtJBerezovskiM. Waves in microstructured solids: A unified viewpoint of modeling. Acta Mech2011; 220: 349–363.
43.
EngelbrechtJBerezovskiAPastroneF. Waves in microstructured materials and dispersion. Phil Mag2005; 85: 4127–4141.
44.
Dell’IsolaFSeppecherPMadeoA. How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Z Angew Math Phys2012; 63(6): 1119–1141.
45.
RosiGGiorgioIEremeyevVA. Propagation of linear compression waves through plane interfacial layers and mass adsorption in second gradient fluids. Z Angew Math Mech2013; 93(12): 914–927.
46.
CazzaniAMalagÃ1MTurcoE. Isogeometric analysis of plane-curved beams. Math Mech Solid2014. Epub ahead of print 20 April 2014. DOI: 10.1177/1081286514531265.
47.
GrecoLCuomoM. An implicit G1 multi patch B-spline interpolation for Kirchhoff–Love space rod. Comput Meth Appl Mech Eng2014; 269: 173–197.
48.
LuongoAZulliDPiccardoG. A linear curved-beam model for the analysis of galloping in suspended cables. J Mech Mater Struct2007; 2(4): 675–694.
49.
LuongoAPiccardoG. A continuous approach to the aeroelastic stability of suspended cables in 1:2 internal resonance. J Vib Contr2008; 14(1–2): 135–157.
