Acoustoelastic analysis has usually been applied to compressible engineering materials. Many materials (e.g., rubber and biologic materials) are “nearly” incompressible and often assumed incompressible in their constitutive equations. These material models do not admit dilatational waves for acoustoelastic analysis. Other constitutive models (for these materials) admit compressibility but still do not model dilatational waves with fidelity (shown herein). In this article a new strain energy function is formulated to model dilatational wave propagation in nearly incompressible, isotropic materials. This strain energy function requires four material constants and is a function of Cauchy–Green deformation tensor invariants. This function and existing (compressible) strain energy functions are compared based upon their ability to predict dilatational wave propagation in uniaxially prestressed rubber. Results demonstrate deficiencies in existing functions and the usefulness of our new function for acoustoelastic applications. Our results also indicate that acoustoelastic analysis has great potential for the accurate prediction of active or residual stresses in nearly incompressible materials.
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November 2005
Technical Papers
New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials
H. Kobayashi,
H. Kobayashi
Department of Engineering Physics, Department of Biomedical Engineering, Department of Orthopedics and Rehabilitation,
University of Wisconsin—Madison
, 600 Highland Avenue, Madison, WI 53792
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R. Vanderby
R. Vanderby
Department of Engineering Physics, Department of Biomedical Engineering, Department of Orthopedics and Rehabilitation,
e-mail: vanderby@surgery.wisc.edu
University of Wisconsin—Madison
, 600 Highland Avenue, Madison, WI 53792
Search for other works by this author on:
H. Kobayashi
Department of Engineering Physics, Department of Biomedical Engineering, Department of Orthopedics and Rehabilitation,
University of Wisconsin—Madison
, 600 Highland Avenue, Madison, WI 53792
R. Vanderby
Department of Engineering Physics, Department of Biomedical Engineering, Department of Orthopedics and Rehabilitation,
University of Wisconsin—Madison
, 600 Highland Avenue, Madison, WI 53792e-mail: vanderby@surgery.wisc.edu
J. Appl. Mech. Nov 2005, 72(6): 843-851 (9 pages)
Published Online: February 11, 2005
Article history
Received:
October 6, 2003
Revised:
February 11, 2005
Citation
Kobayashi, H., and Vanderby, R. (February 11, 2005). "New Strain Energy Function for Acoustoelastic Analysis of Dilatational Waves in Nearly Incompressible, Hyper-Elastic Materials." ASME. J. Appl. Mech. November 2005; 72(6): 843–851. https://doi.org/10.1115/1.2041661
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