Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities

In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1–S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1–S2 and S2–S4 mode pairs are found by using these hyperelastic material models.It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo–Hooke and Mooney–Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.

[1]  I. N. Sneddon,et al.  Finite Deformation of an Elastic Solid , 1954 .

[2]  H. Lamb.  On waves in an elastic plate , 1917 .

[3]  M. Mooney.  A Theory of Large Elastic Deformation , 1940 .

[4]  Kyung-Young Jhang,et al.  Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review , 2009 .

[5]  Qing Zhang,et al.  Numerical Simulation of Nonlinear Lamb Waves Used in a Thin Plate for Detecting Buried Micro-Cracks , 2014, Sensors.

[6]  Laurence J. Jacobs,et al.  Evaluation of fatigue damage using nonlinear guided waves , 2009 .

[7]  Jan Drewes Achenbach,et al.  Detection of thermal fatigue in composites by second harmonic Lamb waves , 2012 .

[8]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[9]  Laurence J. Jacobs,et al.  Modal preference of cumulative second harmonic generation in Lamb waves , 2012 .

[10]  Jing Lin,et al.  Feature Extraction Based on Morlet Wavelet and its Application for Mechanical Fault Diagnosis , 2000 .

[11]  Laurence J. Jacobs,et al.  Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate , 2011 .

[12]  Faramarz Gordaninejad,et al.  Switching band-gaps of a phononic crystal slab by surface instability , 2015 .

[13]  K. Bathe.  Finite-Elemente-Methoden , 1986 .

[14]  Laurence J. Jacobs,et al.  Experimental investigation of symmetry properties of second harmonic Lamb waves , 2012 .

[15]  D. W. Saunders,et al.  Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[16]  M. Deng,et al.  Assessment of accumulated fatigue damage in solid plates using nonlinear Lamb wave approach , 2007 .

[17]  Rolf Lammering,et al.  Impact Damage Detection in Composite Structures Considering Nonlinear Lamb Wave Propagation , 2015 .

[18]  M. Deng.  Cumulative second-harmonic generation of Lamb-mode propagation in a solid plate , 1999 .

[19]  L. Jacobs,et al.  Evaluation of plasticity driven material damage using Lamb waves , 2007 .

[20]  Igor Yu. Solodov,et al.  Ultrasonics of non-linear contacts: propagation, reflection and NDE-applications , 1998 .

[21]  Ping Wang,et al.  Experimental verification of cumulative growth effect of second harmonics of Lamb wave propagation in an elastic plate , 2005 .

[22]  M. Deng.  Analysis of second-harmonic generation of Lamb modes using a modal analysis approach , 2003 .

[23]  C. Truesdell,et al.  Review: F. D. Murnaghan, Finite deformation of an elastic solid , 1952 .

[24]  Mark F. Hamilton,et al.  Finite amplitude waves in isotropic elastic waveguides with arbitrary constant cross-sectional area , 2005 .