Experimental and Computational Methods for the Analysis of the Mechanical Function of Marine Mammal Auditory Structures /
- Author(s): Oberrecht, Stephen Patrick
- et al.
Methods exploring the role of viscoelastic material characterization in vibroacoustic simulations of marine mammal structural responses are presented. This work is guided by a sensitivity analysis performed using the Vibroacoustic Toolkit VATK. In this sensitivity study, computational results are compared with published experimental results arising from the 1974 efforts of Kenneth S. Norris and George W. Harvey. Experimental efforts include the development, calibration, and testing of a portable dynamical mechanical rheometer. For each sample tested the Young's modulus, shear modulus, and viscosity are sought. Mechanical forces, less than a pound, are applied to the tissue through an adhesive interfacial layer. A post-processing routine is developed and results are evaluated. Certain anisotropic elastic materials, such as the homogenized model of a fiber-reinforced matrix, are nearly rigid under stresses applied in a direction of material rigidity--the resulting strains are comparatively small when viewed against the strains that would occur in response to otherwise directed stresses. Isotropic materials may have dilational rigidity, which we show to be a special case of this generalized treatment. Some common finite element techniques are effective in dealing with volumetric locking, but are not suited to handle anisotropic materials that lock under non-hydrostatic stress states. The failure of the traditional B-bar method is attributable to the fundamental assumption that the mode of deformation to be relieved is one of near incompressibility. The proposed remedy exploits the spectral decomposition of the compliance matrix of the anisotropic material. The spectrum separates nearly-rigid and flexible modes of stress and strain leading naturally to a generalized selective reduced integration. What's more, this decomposition also enables a three-field formulation, of elastic strain energy conservation, which results in a B-bar method applicable to general anisotropic materials with nearly-rigid fibers. When materials with multiple rigid fiber directions are treated with more than one spectrally defined deformation mode, element stabilization may be necessary. A working stabilization method is provided. This stabilization leads to a variable treatment model that also offers improved performance for isotropic materials that do not have rigid strain modes