Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

DOI10.1016/j.ijengsci.2010.09.002zbMath1231.74043OpenAlexW2133227358MaRDI QIDQ660631

Yuliya Gorb, Jay R. Walton

Publication date: 4 February 2012

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ijengsci.2010.09.002

zbMATH Keywords

nonlinear elasticityresidual stressIVUSneo-Hookeansmall amplitude high frequency time harmonic vibrationsvulnerable and stable atherosclerotic plaque

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Vibrations in dynamical problems in solid mechanics (74H45) Biophysics (92C05) Biomechanical solid mechanics (74L15)

Related Items (5)

Reconstruction of the residual stresses in a hyperelastic body using ultrasound techniques ⋮ Reconstruction of nonuniform residual stress for soft hyperelastic tissue via inverse spectral techniques ⋮ Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique ⋮ On compressible versions of the incompressible neo-Hookean material ⋮ Stability of classical shock fronts for compressible hyperelastic materials of Hadamard type

Cites Work

• Unnamed Item
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• Sufficient conditions for strong ellipticity for a class of anisotropic materials
• On strong ellipticity for isotropic hyperelastic materials based upon logarithmic strain
• On the residual stress possible in an elastic body with material symmetry
• Secondary deformation due to axial shearing of a cylinder of non-circular cross-section
• Convexity conditions and existence theorems in nonlinear elasticity
• Residual stress in an elastic body: A theory for small strains and arbitrary rotations
• The dependence of the elasticity tensor on residual stress
• A comparison of the response of isotropic inhomogeneous elastic cylindrical and spherical shells and their homogenized counterparts
• On the determination of residual stress in an elastic body
• On uniqueness for the traction problem in finite elasticity
• The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials
• An introduction to continuum mechanics
• Theory of small on large: Potential utility in computations of fluid-solid interactions in arteries
• Plane deformations of elastic solids with intrinsic boundary elasticity
• The Use of Strain Energy to Quantify the Effect of Residual Stress on Mechanical Behavior
• The Convexity Properties of a Class of Constitutive Models for Biological Soft Issues
• Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
• An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity
• Physically based strain invariant set for materials exhibiting transversely isotropic behavior
• A new constitutive framework for arterial wall mechanics and a comparative study of material models

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