Nonlinear Elasticity and Time Reversal Acoustics for Damage

Nonlinear Elasticity and Time Reversal Acoustics for Damage Detection and Localization Michele Griffa, Ph. D. EES-11 (Geophysics) Group Earth and Environmental Sciences (EES) Division Los Alamos National Laboratory MS D 443, Los Alamos, New Mexico, 87545, USA and Bioinformatics and High Performance Computing Lab Biondustry Park of Canavese Colleretto Giacosa (Torino), 10010, Italy Email: mgriffa@lanl. gov Web site: http: //www. lanl. gov/orgs/ees 11/geophysics/staff/griffa. shtml Personal Web site: http: //www. calcolodistr. altervista. org/en/index_en. html UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

About myself. . . MS in Theoretical Physics (2003), University of Torino, Torino (Italy) Majors in Computational Physics and Applied Mathematics Minors in Microelectronics and Cybernetics Thesis field: Mathematical Biology and Biomechanics of Cancer Growth Thesis title: “The Role of Mechanical Pressure, Cellular Adhesion and Apoptosis in the Growth of Multicellular Tumor Spheroids: Physical-Mathematical Modeling” Ph. D. in Physics (2007), Polytechnic Institute of Torino, Torino (Italy) Majors in Condensed Matter Physics and Computational Physics Minors in Biomechanics and Biomathematics Thesis field: Elastodynamics, Nonlinear Elasticity, Ultrasound Imaging, NDE, High Performance Computing (Parallel Programming, Cluster Computing) Thesis title: “Modeling and Numerical Simulation of Elastic Wave Propagation for the Characterization of Complex Heterogeneous Materials” Post Doc (since 2007), Nonlinear Elasticity/Time Reversal Team, EES-11 (Geophysics), Los Alamos National Laboratory, Los Alamos (USA) Research fields: Nonlinear Elasticity, Time Reversal Acoustics, Ultrasonic and Seismic Imaging, NDE, High Performance Computing (Parallel Programming and Cluster Computing) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

About myself. . . Research Projects and Collaborations Nonlinear Acoustics TEchniques for MIcro-Scale damage diagnostics (NATEMIS), European Science Foundation, 2000 - 2005 Integrated Tool for In Situ Characterization of Effectiveness and Durability of Conservation Techniques in Historical Structures (DIAS), EU 5 th Framework Program (FP 5), 2002 - 2005 Nonlinear Elastic Wave Spectroscopy for health monitoring of aircraft (AERONEWS), EU 6 th Framework Program (FP 6), 2004 - 2008 Imaging by Time Reversal Mirrors, Los Alamos National Laboratory, LDRD (Institutional Program), Departmenf of Energy, 2006 - 2009 Department of Physics, Polytechnic Institute of Torino: external collaborator Center for the Development of a VIrtual Tumor (CVIT), Integrative Cancer Biology Program (ICBP), NCI-NIH, USA, 2004 - 2008 Bioinformatics and High Performance Computing Lab, Bioindustry Park of Canavese: external collaborator Aethia Power Computing Solutions, S. r. l. : external collaborator Italian National Institute for Condensed Matter Physics, Parallel Computing Inititative UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Non-Classical Non-Linear (NCNL) Elasticity: the origins General observation: “granular” geomaterials exhibit a peculiar set of nonlinear elastic behaviors, both in the quasi-static (stress-strain equation of state) and dynamic (wave propagation) regimes. Photomicrograph of a 30 m-thick slice of a Berea sandstone obtained by cross-polarized light. Grains with size from 50 to 200 m. R. Guyer, P. A. Johnson, Phys. Today 52 (4), 30 -36 (1999) Nonlinear elastic behaviour of “granular” geomaterials not describable by the “classical” theory of anharmonicity at finite strain amplitudes. UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Quasi-Static Stress-Strain Eq. of State (Eo. S) R. Guyer, P. A. Johnson, Phys. Today 52 (4), 30 -36 (1999) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonlinear Wave Mixing Nonlinear wave mixing experiment: intermediate amplitude sine-wave excitation at low frequency f 1 (pump wave); high-level amplitude excitation at high frequency f (probe wave); f >> f 2 2 1 the amplitude of the pump wave is increased. input: output: A special kind of nonlinear wave mixing: harmonics generation UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonlinear Wave Mixing: an example undamaged plexiglass: elastically linear and isotropic damaged plexiglass: elastically nonlinear, locally anisotropic R. A. Guyer, P. A. Johnson, Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials, Phys. Today 52 (4), 30 -36, 1999. damage due to cyclic loading → induction of pre-stress and change in the structure Classical Nonlinear Wave Mixing classical elastic behaviour <--> “atomic” elastic behaviour the macroscopic deformation properties depend only upon atomic and/or molecular scales bonding and structure: classical elastic behaviour emerges from the microscopic scale UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonlinear Wave Mixing: a more interesting example harmonics generation and nonlinear wave mixing already in the undamaged state and at low strain richer (“classical”) nonlinear frequency spectrum [P. A. Johnson, B. Zinszner and P. N. J. Rasolofosaon, J. Geophys. Res. 101, p. 11553 (1996)] [R. A. Guyer and P. A. Johnson, Physics Today 52, p. 30 (1999)] UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonlinear Wave Mixing: an even more interesting example 2 nd order sidebands f 2 - f 1 f 2 - 2 f 1 R. A. Guyer, P. A. Johnson, Nonlinear Mesoscopic Elasticity, Wiley, to be published f 2 + f 1 f 2 + 2 f 1 not predicted by the classical theory of Nonlinear Elasticity but. . . predicted in the framework of Nonclassical Nonlinear Elasticity UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity: where does it come from ? ? Which materials do exhibit such anomalous elastic behaviour porous aluminum powder soil (sieved, typical grain size 1 mm) sandstone (typical grain size ~ 100 m) concrete ceramic UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity: where does it come from ? ? Which materials do exhibit such anomalous elastic behaviour typical structure: hard matrix made by many “grains” cemented together by “soft” inclusions (fluids, gels, or dislocation -based kinking bands) multi-phase materials micro-structured materials mesoscopic elasticity the “bond system” (set of soft inclusions) determines the presence and the level of nonclassical nonlinear elastic behavior water saturation levels (Carmeliet and Van Den Abeele, 2002) mechanics of contact interfaces phases and types of media constituting the “bond system” (neutron scattering experiments at LANL, Ten Cate and Darling, 2004 -2007) nanoindentation and creation of dislocation-based kink bands (Barsoum et al. , 2004 -2008) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity: where does it come from ? ? Which materials do exhibit such anomalous elastic behaviour pyrex containing cracks; marble; pearlite/graphite metal; alumina ceramic; sintered metal; Perovskite ceramic; quartzite; damaged concrete; metallic solids with interconnected dislocation networks, cracks or creeps; nanoindented graphite, sapphire, layered semiconductors (in general MAX phases) experimental evidence of nonclassical nonlinear elastic phenomenology in others materials only when damaged damage change in structure UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity and NDE: damage detection looking for nonclassical nonlinear elastic behaviors as fingerprints of damage: damage detection Nonlinear Elastic Wave Spectroscopy (NEWS) K. Van Den Abeele et al. , Res. Nondestr. Eval. 12, 17 -42 (2000) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Understanding and Exploiting Nonclassical Nonlinear Elasticity: modeling and numerical simulations for supporting basic and applied experimental investigations need of a physical theory of NCNL Elasticity based on the knowledge of the micromechanics NCNL elastic solids as a subcategory of Nonlinear Kinking Solids (Barsoum et al. , 20042008) LISA modeling + Preisach. Mayergoyz phenomenological modeling UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

LISA (Local Interaction Simulation Approach) for elastic wave propagation in solids beyond traditional FDTD (Finite Differences Time Domain) for solving differential problems of Elastodynamics Features: based on a full displacement explicit FDTD scheme for solving PDEs; exploitation of the mathematical correspondence between FDTD numerical discretization of PDEs and analogical modeling with discrete coupled systems (lumped-masses); mimetic scheme; possibility of introducing in the model phenomenological “laws” of interactions between representative particles and/or special elastic behaviors of springs; developed for modeling elastic wave propagation throughout highly heterogeneous materials, i. e. with a huge number of interfaces (M. Scalerandi, P. P. Delsanto et al. , Naval Research Lab, USA, and Polytechnic Institute of Torino, Italy) modeling the physical role of interfaces in the wave propagation mechanism beyond simple reflection/refraction behavior ---> giving a physical “existence” to interfaces within the model UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

LISA-Spring Modeling Approach the importance of the mechanical behavior of the interstices constituting the “binding medium” grains <---> Kelvin-Voigt's viscoelastic bodies interstices/bond system modeling internal forces between interstices imposing constraints on the dynamics of the lateral sides of the interfaces LISA modeling approach LISA-Spring modeling approach poro-viscoelastic bodies with two possible sets of values for their parameters <--> two possible “states” dynamic switching between the two states during the wave propagation according to the comparison of a “control” parameter versus thresholds UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

LISA-Spring Modeling Approach each interstice is an the whole specimen HEE (Hysteretic Elastic contains a huge amount of Elements), characterized HEEs into the by a mapped bi-state dynamics Preisach-Mayergoyz plane triggered by the (Pporo-elastic pressure P; c, Po); each HEEelastic is the overall behavior the of characterized the whole specimen accounting forby hysteretic couple of from threshold “emerges” the local strain-stress constitutive values for (PHEEs; , P ) dynamics of P, the c o relations for “granular” materials geomaterials M. Scalerandi, P. P. Delsanto, Phys. Rev. B 68 (6), 64107 -1 -9 (2003) M. Scalerandi et al. , J. Acoust. Soc. Amer. 113 (6), 3049 -59 (2003) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity of Damaged Concrete In collaboration with M. Bentahar, R. El Guerjouma, GEMPPM UMR CNRS and INSA Lyon ≈ 168. 2 KHz M. Bentahar, H. El Aqra, R. El Guerjouma, M. Griffa, M. Scalerandi, Phys. Rev. B 73, 014116 (2006) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity of Damaged Concrete M. Bentahar, H. El Aqra, R. El Guerjouma, M. Griffa, M. Scalerandi, Phys. Rev. B 73, 014116 (2006) linear regime logarithmic-in-time recovery (slow dynamics) greater time recovey in the case of the damaged specimen UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity of Damaged Concrete the problem of damage detection Two possible very sensitive to the damage state. Spectroscopy of a specimen linear (smallobservables excitation amplitude) Resonant Ultrasound (i. e. to the nonlinear nonclassical elastic behaviour): (RUS) measurements are already sensitive to the presence of damage (10% relative shift therelative resonance frequency), but they always require aamplitude reference slope ofofthe resonance frequency shift vsin output peak linear regime resonance frequency recovery time slow dynamics intact specimen ! conditioning (small, reversible, changes of the elastic properties of the intersticial media even when a small amplitude perturbing wave is injected into the specimen) is at the basis of the fast and slow dynamics phenomenology -----> from the modeling of interstices elastic properties. the validation of the model confirms the bases of its mathematical description of mechanisms for changes in elastic parameters of interstices, but the physical processes and components responsible for these changes must be discovered in order to develop a successful theory of NCNL Elasticity. UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity and NDE the problem of damage localization LISA-Spring 2 D simulation of elastic wave propagation in an Al sample with a linear inhomogeneity and a NCNL damage area (thin micro-crack) A. S. Gliozzi, M. Griffa, M. Scalerandi, Efficiency of Time-Reversed Acoustics for Nonlinear Damage Detection in Solids, J. Acous. Soc. Amer. 120 (5), 2506 -2517, (2006) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity and NDE the problem of damage localization LISA-Spring 2 D simulation of elastic wave propagation in an Al sample with a linear inhomogeneity and a NCNL damage area (thin micro-crack) A. S. Gliozzi, M. Griffa, M. Scalerandi, Efficiency of Time-Reversed Acoustics for Nonlinear Damage Detection in Solids, J. Acous. Soc. Amer. 120 (5), 2506 -2517, (2006) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity and NDE the problem of damage localization Inserisci qui l'ultimo snapshots dal movie precedente weak scattering by the linear inhomogeneity even more weak scattering by the very thin NCNL feature (the damage region) how to solve the inverse scattering problem and localize (image) selectively the different types of defects (linear and nonlinear) ? UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Imaging by Time Reversal Acoustics M. Fink, Scientific American 281 (5), 91 -97 (1999) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

general linear Elastodynamics wave equation covariance in respect of t --> -t P. Roux, B. Roman, M. Fink, Time Reversal in an ultrasonic waveguide, Appl. Phys. Lett. 70 (14), 1811 -1813 (1997) spatial retro-focusing; temporal compression; multiple reflections subtitute TR transducers; spatial information converted into temporal information; A. Derode, P. Roux, M. Fink, Robust Acoustic Time Reversal with High-Order Multiple Scattering, Phys. Rev. Lett 75 (3), 4206 -4210 (1995) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Nonclassical Nonlinear Elasticity and NDE the problem of damage localization TR-NEWS: Time Reversal + Nonlinear Elastic Wave Spectroscopy insonify the specimen (forward propagation, FP) collect the signals at the Time Reversal Mirror apply NEWS signal processing to enhance the nonlinear scatterer contribution time reverse and rebroadcast into the specimen the signals perform the TR backward propagation, experimentally for surface damage detection, in silico for 3 D embedded UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

The problem of damage localization TR backward propagation with removal of the base-line (reflections from the boundaries and contribution of the inspection sources): focusing at the linear scatterer location A. S. Gliozzi, M. Griffa, M. Scalerandi, Efficiency of Time-Reversed Acoustics for Nonlinear Damage Detection in Solids, J. Acous. Soc. Amer. 120 (5), 2506 -2517, (2006) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

TR-NEWS imaging: simulation test TR backward propagation with removal of the base-line + NEWS filtering: focusing at the nonlinear scatterer location only A. S. Gliozzi, M. Griffa, M. Scalerandi, Efficiency of Time-Reversed Acoustics for Nonlinear Damage Detection in Solids, J. Acous. Soc. Amer. 120 (5), 2506 -2517, (2006) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

TR-NEWS imaging of surface micro-cracks: experimental results Sources: broadband -- hammer tap (excite 4 k. Hz) probe – 204 k. Hz, toneburst (200 cycles, sin 2 envelope) T. J. Ulrich et al. , Phys. Rev. Lett. 98, 104301 (2007) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

3 D TR imaging UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Additional information LANL Nonlinear Elasticity Web site http: //www. lanl. gov/orgs/ees 11/geophysics/nonlinear. shtml LANL Time Reversal Acoustics in solid media Web site: http: //www. lanl. gov/orgs/ees 11/geophysics/timerev. shtml B. E. Anderson, M. Griffa, C. Larmat, T. J. Ulrich, P. A. Johnson, Acoustics Today 4 (1), 5 -16 (2008) UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX

Thanks a lot for your attention UNCLASSIFIED Operated by Los Alamos National Security, LLC for NNSA LAUR 2008 -XX-XX