The need to account for residual strains and composite nature of heart wall in mechanical analyses

1996 ◽  
Vol 271 (3) ◽  
pp. H947-H961 ◽  
Author(s):  
T. Kang ◽  
F. C. Yin
Keyword(s):  
Strain Energy ◽  
Left Ventricular ◽  
Energy Functions ◽  
Mechanical Responses ◽  
Residual Strains ◽  
Composite Nature ◽  
Strain Energy Functions ◽  
Heart Wall ◽  
Strain Responses ◽  
Canine Myocardium

We studied 19 excised, passive rabbit left ventricular walls to delineate the forms of the strain-energy functions (W) for myocardium and epicardium, to quantify residual strains across the wall, and to investigate whether the mechanical behavior of the intact wall can be predicted by accounting for the above properties. The unloaded dimensions and the stress-strain responses to equibiaxial and uniaxial loadings were obtained first for the intact wall and then individually for the epicardium and myocardium. Results show that the previously proposed W for canine myocardium and epicardium are suitable. The unloaded intact wall has residual strains: the epicardium is stretched and the myocardium shrunk from their respective isolated, unloaded states. The predicted mechanical responses of the intact wall to biaxial loadings were inaccurate when the residual strains were not taken into account. Accounting for these, however, yielded reasonable predictions. Thus information on the unloaded reference state and properties of each portion is needed to accurately predict the behavior of the intact wall.

scholarly journals Left Ventricular Endocardium Tracking by Fusion of Biomechanical and Deformable Models

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hussin Ketout ◽  
Jason Gu
Keyword(s):  
Gold Standard ◽  
Strain Energy ◽  
Cardiac Cycle ◽  
Image Sequence ◽  
Left Ventricular ◽  
Deformable Model ◽  
Energy Functions ◽  
Echocardiography Image ◽  
2D Echocardiography ◽  
Strain Energy Functions

This paper presents a framework for tracking left ventricular (LV) endocardium through 2D echocardiography image sequence. The framework is based on fusion of biomechanical (BM) model of the heart with the parametric deformable model. The BM model constitutive equation consists of passive and active strain energy functions. The deformations of the LV are obtained by solving the constitutive equations using ABAQUS FEM in each frame in the cardiac cycle. The strain energy functions are defined in two user subroutines for active and passive phases. Average fusion technique is used to fuse the BM and deformable model contours. Experimental results are conducted to verify the detected contours and the results are evaluated by comparing themto a created gold standard. The results and the evaluation proved that the framework has the tremendous potential to track and segment the LV through the whole cardiac cycle.

Strain energy functions for filled elastomers

1965 ◽  
Vol 9 (7) ◽  
pp. 2565-2579 ◽  
Author(s):  
M. Shinozuka ◽  
A. M. Freudenthal
Keyword(s):  
Strain Energy ◽  
Energy Functions ◽  
Filled Elastomers ◽  
Strain Energy Functions

On the Development of Volumetric Strain Energy Functions

1999 ◽  
Vol 67 (1) ◽  
pp. 17-21 ◽  
Author(s):  
S. Doll ◽  
K. Schweizerhof
Keyword(s):  
Strain Energy ◽  
Volumetric Strain ◽  
Strain Energy Function ◽  
Material Behavior ◽  
Additional Material ◽  
Energy Functions ◽  
Material Parameters ◽  
Physical Conditions ◽  
Starting Point ◽  
Strain Energy Functions

To describe elastic material behavior the starting point is the isochoric-volumetric decoupling of the strain energy function. The volumetric part is the central subject of this contribution. First, some volumetric functions given in the literature are discussed with respect to physical conditions, then three new volumetric functions are developed which fulfill all imposed conditions. One proposed function which contains two material parameters in addition to the compressibility parameter is treated in detail. Some parameter fits are carried out on the basis of well-known volumetric strain energy functions and experimental data. A generalization of the proposed function permits an unlimited number of additional material parameters.  Dedicated to Professor Franz Ziegler on the occasion of his 60th birthday. [S0021-8936(00)00901-6]

Finding the Constitutive Relation for a Specific Elastomer

1993 ◽  
Vol 115 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Yun Ling ◽  
Peter A. Engel ◽  
Wm. L. Brodskey ◽  
Yifan Guo
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Strain Energy ◽  
Pure Shear ◽  
Strain Energy Function ◽  
Invariant Polynomial ◽  
Energy Functions ◽  
Finite Element Program ◽  
Biaxial Extension ◽  
Strain Energy Functions

The main purpose of this study was to determine a suitable strain energy function for a specific elastomer. A survey of various strain energy functions proposed in the past was made. For natural rubber, there were some specific strain energy functions which could accurately fit the experimental data for various types of deformations. The process of determining a strain energy function for the specific elastomer was then described. The second-order invariant polynomial strain energy function (James et al., 1975) was found to give a good fit to the experimental data of uniaxial tension, uniaxial compression, equi-biaxial extension, and pure shear. A new form of strain energy function was proposed; it yielded improved results. The equi-biaxial extension experiment was done in a novel way in which the moire techniques (Pendleton, 1989) were used. The obtained strain energy functions were then utilized in a finite element program to calculate the load-deflection relation of an electrometric spring used in an electrical connector.

Neural Network Based Constitutive Model for Rubber Material

2004 ◽  
Vol 77 (2) ◽  
pp. 257-277 ◽  
Author(s):  
Y. Shen ◽  
K. Chandrashekhara ◽  
W. F. Breig ◽  
L. R. Oliver
Keyword(s):  
Neural Network ◽  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Phenomenological Approach ◽  
Neural Network Approach ◽  
Energy Functions ◽  
The Neural Network ◽  
Strain Energy Functions

Abstract Rubber hyperelasticity is characterized by a strain energy function. The strain energy functions fall primarily into two categories: one based on statistical thermodynamics, the other based on the phenomenological approach of treating the material as a continuum. This work is focused on the phenomenological approach. To determine the constants in the strain energy function by this method, curve fitting of rubber test data is required. A review of the available strain energy functions based on the phenomenological approach shows that it requires much effort to obtain a curve fitting with good accuracy. To overcome this problem, a novel method of defining rubber strain energy function by Feedforward Backpropagation Neural Network is presented. The calculation of strain energy and its derivatives by neural network is explained in detail. The preparation of the neural network training data from rubber test data is described. Curve fitting results are given to show the effectiveness and accuracy of the neural network approach. A material model based on the neural network approach is implemented and applied to the simulation of V-ribbed belt tracking using the commercial finite element code ABAQUS.

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