An energy density function for papillary muscle encompassing both elastic and contractile properties

1981 ◽  
Vol 52 (5) ◽  
pp. 3674-3687 ◽  
Author(s):  
Willem Klip ◽  
Lloyd L. Hefner ◽  
Thomas C. Donald ◽  
David N. S. Reeves ◽  
Jane B. Hazelrig ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Papillary Muscle ◽  
Contractile Properties

The strain energy density function

1986 ◽  
pp. 237-253
Author(s):  
G. C. Sih ◽  
J. G. Michopoulos ◽  
S. C. Chou
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Strain Energy Density Function

Folding deformation modeling and simulation of 4D printed bilayer structures considering the thickness ratio

2019 ◽  
Vol 25 (2) ◽  
pp. 348-361 ◽  
Author(s):  
Zhenyu Liu ◽  
Han Liu ◽  
Guifang Duan ◽  
Jianrong Tan
Keyword(s):  
Energy Density ◽  
Modeling And Simulation ◽  
Density Function ◽  
Thickness Ratio ◽  
Equivalent Transformation ◽  
Deformation Model ◽  
Bilayer Structure ◽  
Bending Deformation ◽  
Stretching Deformation ◽  
Deformation Models

This paper addresses the problem of deformation modeling and simulation of 4D printed polymeric bilayer structures considering the thickness ratio. Through an equivalent transformation, the folding deformation model is transformed into two simpler deformation models, stretching and bending, which greatly reduces the complexity of the modeling problem. The stretching deformation model is developed by Hooke’s law, and based on the final strain of the stretching deformation, which is determined by the thickness ratio, a new hyperelastic energy density function considering the thickness ratio is defined to calculate the energy of the bilayer structure during the bending deformation. According to the new energy density function, the bending deformation model considering the thickness ratio is developed by minimizing the energy of the bilayer structure during the bending deformation. Numerical simulations show encouraging results obtained by the proposed model.

An adaptive meshing automatic scheme based on the strain energy density function

1997 ◽  
Vol 14 (6) ◽  
pp. 604-629 ◽  
Author(s):  
A. Hernández ◽  
J. Albizuri ◽  
M.B.G. Ajuria ◽  
M.V. Hormaza
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Adaptive Meshing ◽  
Strain Energy Density Function

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
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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