A Large-Deformation Finite-Element Analysis for Multilayer Elastomeric Bearings

Abstract Finite element methods are applied for multilayer elastomeric bearings under large deformation. The method is capable of handling nonlinear elasticity and incompressibility of rubber-like materials. The strain energy density function which determines elastic properties of the materials is obtained empirically through strip biaxial testing. The computation using the strain energy density function is conducted to analyze the stress and strain distribution and the performance characteristics of multilayer elastomeric bearings, which is in good agreement with the results of actual experiments.

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Large Deformation Analysis of the Arterial Cross Section

Journal of Basic Engineering ◽

10.1115/1.3425199 ◽

1971 ◽

Vol 93 (2) ◽

pp. 138-145 ◽

Cited By ~ 23

Author(s):

B. R. Simon ◽

A. S. Kobayashi ◽

D. E. Strandness ◽

C. A. Wiederhielm

Keyword(s):

Finite Element ◽

Energy Density ◽

Numerical Integration ◽

Density Function ◽

Cross Section ◽

Finite Deformation ◽

Strain Energy Density ◽

Strain Energy ◽

Exponential Form ◽

Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

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Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

Journal of Biomechanical Engineering ◽

10.1115/1.4036440 ◽

2017 ◽

Vol 139 (7) ◽

Cited By ~ 6

Author(s):

Zaw Win ◽

Justin M. Buksa ◽

Kerianne E. Steucke ◽

G. W. Gant Luxton ◽

Victor H. Barocas ◽

...

Keyword(s):

Energy Density ◽

Density Function ◽

Strain Energy Density ◽

Strain Energy ◽

Mechanical Stimulus ◽

Elastic Behavior ◽

Biaxial Testing ◽

Cellular Mechanics ◽

Biomechanical Models ◽

Strain Energy Density Function

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel–Gasser–Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

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