The advent of large memory fast computers in the late 1980s encouraged the development of numerical simulation of stress wave propagation under conditions where exact solutions are not possible. A few investigators were interested in studying problems where elastic anisotropy resulted in models of complex phenomena that exist within large three-dimensional structures. The massive output of results from these simulations, together with the added complexity of coupled phenomena that uniquely exist for a given anisotropy, defies intuition. To grasp the physical significance of these numerical simulations requires visual data analysis in an animated format.
Two Russian researchers, [Merkulov and Yakovlev, 62] where the first to experimentally-visually demonstrate the influence of elastic anisotropy on the energy propagation deviation in two-dimensions by the use of Schlieren. This technique is applicable only for transparent media such as Quartz. For anisotropic media that is opaque it is possible to study the influence of anisotropy on energy deviation by developing simulation-visualization techniques that reveal complex phenomena difficult if not impossible to measure. First we show how to experimentally measure this energy deviation in an opaque graphite-epoxy material by lateral movement of the receiving transducer at the outer boundary [Kriz-Stinchcomb, 75]. With a full field simulation and visualization we can also study the physics of these phenomena in the interior. An interactive visual tool was developed to study how degradation in either the fiber (graphite) component or matrix (epoxy) component could be used to measure preferential component degradation in a unidirectional composite. With full field simulation results it is possible to study the shear and longitudinal components of QL and QT waves in a finite element mesh [Kriz-Heyliger, 89]. With a higher density finite difference mesh we can more accurately observe continuity of propagating waves but fail to differentiate between shear and logintudinal components [Kriz-Gary, 90]. Changing the fiber orientation can lead to a mode transition of shear and longitudinal components of these waves at a fiber orientation of 51 degrees [Kriz-Vandenbossche, 95]. Here we provide a schematic of our full field simulation that will help us interpret the full field animation where we observe the propagation of a two cycle pulse emanating from the lower boundary. Note that the energy bifurcates into faster moving QL and a slower moving QT components where the reflected QL component reflects back towards the original transmission location without generating another QT wave. Also note that the difference of the QL and QT wavelengths.
We can use this idea to preferentially launching either a QL or QT wave at the boundary. We demonstrated this numerically by launching only the QL wave for a fiber orentation of theta=50 degrees. This same data set was used to create a SIGgraph89 video ( wave.mov (17Mb) / wave.mpg (24Mb)).
Animated sequences of gray scale images were used to observe the deformation fields at various values of theta to characterize the total acoustic response of unidirectional graphite/epoxy: 1) before mode transition (theta less than 50 degrees), 2) near mode transtion (theta=50 degrees), and after mode transition (theta greater than 51 degrees). Here both QL and QT waves are launched as continuous sinusoidal waves over a finite aperature. Theta, degrees: 10, 20, 30, 40, 50, 60. These are rather small animations where the mode transition can not be seen using a gray scale format. However it is possible to see the QT to QL mode transition using a simple deformed mesh and synchronizing the different mesh fiber orientations in a animated small-multiple collage. Closer examination of individual meshs reveals the physical deformations assoicated mode transitions and other complex phenomena assoicated with elastic anisotropy. The development of simulation models of energy flux deviation has been documented and results archived for more detailed analysis.
Closer examimation of simulation results reveal that different wave types are connected in ways not predicted by theory. For example theoretical models of plane wave assume the plane of the waves that exist in the interior extend to infinity and surface waves are isolated near stress free surfaces. Closer examination of simulation results reveal that plane waves launched at a boundary within a finite apperature are connected to surface waves by the diffraction that is created at the edge of the simulated transducers. The numerical simulation is bounded by adjacent parallel boundaries that result in reflections that maintain the mode type and flux deviation angles. Using Gourand shading it possible to see the bimodal structure of the Rayleigh surface waves along with preferential launching QL and QT wave modes, [Kriz-Gary, 90]. All of these phenomena are observed by carefully selecting the appropriate visualization format within the context of how the science is perceived by the researcher. This is why it is important that researchers create both their own mathematical and graphical models.
Merkulov, L.G. and Yakovlev, L.A., "Propagation and Reflection of Ultrasonic Beams in Crystals," Soviet Physics-Acoustics, Vol.8 No.1, pp. 72-77, 1962.
Kriz, R.D. and Stichcomb, W.W., "Elastic Moduli of Transversely Isotropic Graphic Fibers and Their Composite," J. Experimental Mechanics, Vol.19 No.2, pp. 41-49, 1979.
Kriz, R.D. and Heyliger, P.R., "Finite Element Model of Stress Wave Topology in Unidirectional Graphite/Epoxy: Wave Velocities and Flux Deviations," Review of Progress in Quantitative Nondestructive Evaluation, Vol.8A, Plenum Publishing Corp., pp. 141-148, 1989.
Kriz, R.D. and Gary J.M., "Numerical Simulation and Visualization Models of Stress Wave propagation in Graphite/Epoxy Composites," Review of Progress in Quantitative Nondestructive Evaluation, Vol.9, Plenum Publishing Corp., pp. 125-132, 1990.
Vandenbossche, B. and Kriz, R.D.,and Oshima, T., "Stress Wave Displacement Polarizations and Attenuation in Unidirectional Composites: Theory and Experiment," J. Research In Nondestructive Evaluation, Vol.8 No.2, pp. 101-123, 1996.