Physical Invariant Constitutive Equation for Soft Tissues

M.H.B.M. Shariff

doi:10.4028/www.scientific.net/AMM.432.196

Paper Titles

Application of Homotopy Perturbation Method for the Generalized Burgers-Fisher Equation
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Modeling and Analyzing for Multi-Axis Wheeled Vehicle Handling Performance and Stability
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Some Opial Type Inequalities with Higher Order Delta Derivative on Time Scales
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Numerical Investigation of Sub-Iteration Criterions for Unsteady Flow Computations with Dual-Time Method
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Physical Invariant Constitutive Equation for Soft Tissues
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Design Check for the Steel Gusset Plate in Tension Using LRFD Method
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Implementation and Verification of High-Order Accurate Discontinuous Galerkin Method on 2-D Unstructured Grids
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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 432Physical Invariant Constitutive Equation for Soft...

Physical Invariant Constitutive Equation for Soft Tissues

Abstract:

Principal axis formulations are regularly used in isotropic elasticity but they are not often used in dealing with anisotropic problems. In this paper, based on a principal axis technique, we develop a physical invariant constitutive equation for incompressible transversely isotropic solids, where it contains only a one variable (general) function. The corresponding strain energy function depends on four invariants that have immediate physical interpretation. These invariants are useful in facilitating an experiment to obtain a specific constitutive equation for a particular type of materials. The explicit appearance of the classical ground state constants in the constitutive equation simplifies the calculation for their admissible values. A specific constitutive model is proposed for soft tissues and the model fits reasonably well with existing experimental data; it is also able to accurately predict experiment data.

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Periodical:

Applied Mechanics and Materials (Volume 432)

Pages:

196-201

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.432.196

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Online since:

September 2013

Authors:

M.H.B.M. Shariff

Keywords:

Incompressible, Invariants with Immediate Physical Meaning, Principal Axes, Soft Tissues, Strain Energy, Transversely Isotropic

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References

[1] R.W. Ogden, Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A 326 (1972)565-584.

DOI: 10.1098/rspa.1972.0026

Google Scholar

[2] M.H.B.M. Shariff, Strain energy function for filled and unfilled rubberlike material. Rubber Chem. Technol. 73 (2000) 1-21.

DOI: 10.5254/1.3547576

Google Scholar

[3] K.C. Valanis, R.F. Landel, The strain-energy function of hyperelastic material in terms of the extension ratios, J. Appl. Phys. 38 (1967) 2997-3002.

DOI: 10.1063/1.1710039

Google Scholar

[4] M.H.B.M. Shariff, MHBM Nonlinear transversely isotropic elastic solids: an alternative representation, Q. J. Mech. Appl. Math. 61(2) (2008) 129-149.

Google Scholar

[5] A.J.M. Spencer, Constitutive Theory of the Mechanics of Fiber Reinforced Composites, CISM Courses and Lectures No. 282. (1984) Wien: Springer.

Google Scholar

[6] E.J. Weinberg, M.R. Kaazeempur-Mofrad, A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics, J. of Biomech. 39 (2006) 1557-1561.

DOI: 10.1016/j.jbiomech.2005.04.020

Google Scholar

[7] C. Chui, E. Kobayashi, X. Chen, T. Hisada, I. Sakuma, Transversely isotropic properties of porcine liver tissue: experiments and constitutive modeling, Med. Bio. Eng. Comput, 45 (2007) 99-106.

DOI: 10.1007/s11517-006-0137-y

Google Scholar

[8] M.H.B.M. Shariff, Physical invariant strain energy function for passive myocardium, Biomech. Model Mechanobiol. (2012) DOI 10. 1007/s10237-012-0393-8.

DOI: 10.1007/s10237-012-0393-8

Google Scholar

[9] M.H.B.M. Shariff, Physical invariants for nonlinear orthotropic solids, Int. Jou. Solids and Structures 48 (2011) 1906-(1914).

DOI: 10.1016/j.ijsolstr.2011.03.002

Google Scholar