Detection and Modelling of Nonlinear Elastic Response in Damaged Composite Structures

In this paper the nonlinear material response of damaged composite structures under periodic excitation is experimentally and numerically investigated. In particular, the nonlinear wave propagation problem was numerically analysed through a finite element model able to predict the nonlinear interaction of acoustic/ultrasonic waves with damage precursors and micro-cracks. Such a constitutive model is based on the Landau’s semi-analytical approach to account for anharmonic effects of the medium, and is able to provide an understanding of nonlinear elastic phenomena such as the second harmonic generation. Moreover, Kelvin tensorial formulation was used to extend the wave propagation problem in orthotropic materials to the 3D Cartesian space. In this manner, the interaction of the stress waves with the 3D crack could be analysed. This numerical model was then experimentally validated on a composite plate undergone to impact loading. Good agreement between the experimental and numerical second harmonic response was found, showing that this material model can be used as a simple and useful tool for future structural diagnostic applications.

[1]  Lev A. Ostrovsky,et al.  Dynamic nonlinear elasticity in geomaterials , 2001 .

[2]  Alexander Sutin,et al.  Sensitive imaging of an elastic nonlinear wave-scattering source in a solid , 2002 .

[3]  J. Donéa,et al.  Advanced structural dynamics , 1980 .

[4]  Alexander Sutin,et al.  Micro-damage diagnostics using Nonlinear Elastic Wave Spectroscopy (NEWS) , 2001 .

[5]  Pierre-Yves Guerder,et al.  A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation. , 2012, The Journal of the Acoustical Society of America.

[6]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[7]  J. Cantrell,et al.  Fundamentals and Applications of Nonlinear Ultrasonic Nondestructive Evaluation , 2003 .

[8]  Mark F. Hamilton,et al.  Finite-amplitude waves in isotropic elastic plates , 2003 .

[9]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[10]  Jan Carmeliet,et al.  Inferring the degradation of pultruded composites from dynamic nonlinear resonance measurements , 2001 .

[11]  Victor Giurgiutiu,et al.  Piezoelectric Wafer Embedded Active Sensors for Aging Aircraft Structural Health Monitoring , 2002 .

[12]  Peter B. Nagy,et al.  Acoustic nonlinearity in plastics , 1992 .

[13]  C. Pecorari.  Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact. , 2003, The Journal of the Acoustical Society of America.

[14]  Michele Meo,et al.  Damage localization using transient non-linear elastic wave spectroscopy on composite structures , 2008 .

[15]  J. Achenbach,et al.  Higher harmonics in the far field due to dynamic crack‐face contacting , 1993 .

[16]  D. Thompson,et al.  Review of Progress in Quantitative Nondestructive Evaluation , 1982 .

[17]  Jeong-Beom Ihn,et al.  Pitch-catch Active Sensing Methods in Structural Health Monitoring for Aircraft Structures , 2008 .

[18]  P. Johnson,et al.  Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids. , 2003, The Journal of the Acoustical Society of America.

[19]  F. Schubert,et al.  Resonant bar simulations in media with localized damage. , 2004, Ultrasonics.

[20]  R. W. Clayton,et al.  Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity , 2015 .

[21]  A THEORETICAL PARADIGM FOR DESCRIBING HYSTERESIS AND NONLINEAR ELASTICITY IN ARBITRARY ANISOTROPIC ROCKS , 2000 .

[22]  A. Sutin,et al.  Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS) , 2000 .

[23]  Michele Meo,et al.  Nonlinear elastic wave spectroscopy identification of impact damage on a sandwich plate , 2005 .

[24]  Ettore Barbieri,et al.  Time reversal DORT method applied to nonlinear elastic wave scattering , 2010 .

[25]  Francesco Ciampa,et al.  Nonlinear elastic imaging using reciprocal time reversal and third order symmetry analysis. , 2012, The Journal of the Acoustical Society of America.

[26]  Pier Paolo Delsanto,et al.  A spring model for the simulation of the propagation of ultrasonic pulses through imperfect contact interfaces , 1998 .

[27]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[28]  Michele Meo,et al.  A new nonlinear elastic time reversal acoustic method for the identification and localisation of stress corrosion cracking in welded plate-like structures - : A simulation study , 2007 .

[29]  Michele Meo,et al.  A new damage detection technique based on wave propagation for rails , 2006 .

[30]  W. H. Reid,et al.  The Theory of Elasticity , 1960 .

[31]  P. Johnson.  Nonequilibrium Nonlinear Dynamics in Solids: State of the Art , 2006 .

[32]  Ettore Barbieri,et al.  Modelling of multiscale nonlinear interaction of elastic waves with three-dimensional cracks. , 2014, The Journal of the Acoustical Society of America.

[33]  P. Theocaris,et al.  Spectral decomposition of the compliance fourth-rank tensor for orthotropic materials , 2000 .