On the Constitutive Equations of Biological Materials

1975 ◽  
Vol 42 (1) ◽  
pp. 242-243 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Biological Materials ◽  
Biological Tissues

This paper deals with a simple possible form of the strain-energy function for biological tissues which are assumed to be transversely isotropic. Also the solution of a problem is studied and the result is compared with experiments.

On the Choice of Strain Energy Function for Mechanical Characterisation of Soft Biological Tissues

1984 ◽  
Vol 13 (1) ◽  
pp. 11-14 ◽  
Author(s):  
K B Sahay
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Energy Functions ◽  
Soft Biological Tissues ◽  
Mechanical Characterisation ◽  
Strain Energy Functions ◽  
Made In

Constitutive equations that describe stress–strain relations of soft biological tissues require parameters such as the strain energy functions, or certain of their derivatives. An attempt has been made in this paper to examine the suitability of the various strain energy functions reported in the literature. Certain criteria are proposed for the same.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

Finite Elastic Deformation for a Class of Soft Biological Tissues

1977 ◽  
Vol 99 (2) ◽  
pp. 98-103
Author(s):  
Han-Chin Wu ◽  
R. Reiss
Keyword(s):  
Energy Function ◽  
Annulus Fibrosus ◽  
Strain Energy ◽  
Soft Tissues ◽  
Broad Class ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tension Test ◽  
Soft Biological Tissues ◽  
Precise Form

The stress response of soft biological tissues is investigated theoretically. The treatment follows the approach of Wu and Yao [1] and is now extended for a broad class of soft tissues. The theory accounts for the anisotropy due to the presence of fibers and also allows for the stretching of fibers under load. As an application of the theory, a precise form for the strain energy function is proposed. This form is then shown to describe the mechanical behavior of annulus fibrosus satisfactorily. The constants in the strain energy function have also been approximately determined from only a uniaxial tension test.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

2021 ◽  
pp. 1-14
Author(s):  
Takashi Funai ◽  
Hiroyuki Kataoka ◽  
Hideo Yokota ◽  
Taka-aki Suzuki
Keyword(s):  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Stress Strain ◽  
Increasing Trend ◽  
Strain Energy Functions ◽  
Derived Function

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

scholarly journals A generalized strain approach to anisotropic elasticity

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
M. H. B. M. Shariff
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Single Variable ◽  
Energy Functions ◽  
Anisotropic Strain ◽  
Strain Energy Functions ◽  
Strain Function

AbstractThis work proposes a generalized Lagrangian strain function $$f_\alpha$$ f α (that depends on modified stretches) and a volumetric strain function $$g_\alpha$$ g α (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions $$f_\alpha$$ f α and $$g_\alpha$$ g α to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

A Structural Strain Energy Function for Vascular Tissue Considering Elastin Anisotropy

2007 ◽  
Author(s):  
Rana Rezakhaniha ◽  
Nikos Stergiopulos
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Vessel Wall ◽  
Strain Energy ◽  
Vascular Tissue ◽  
Strain Energy Function ◽  
Nonlinear Properties ◽  
Wide Range ◽  
Nonlinear Elastic ◽  
Structural Strain

The vessel wall exhibits relatively strong nonlinear properties and undergoes a wide range of deformations. Identification of a strain energy function (SEF) is the preferred method to describe the complex nonlinear elastic properties of the vascular tissue. Once the strain energy function is known, constitutive equations can be obtained.

Constitutive Equations for Isotropic Rubber-Like Materials Using Phenomenological Approach: A Bibliography (1930–2003)

2006 ◽  
Vol 79 (3) ◽  
pp. 489-499 ◽  
Author(s):  
Vahap Vahapoğlu ◽  
Sami Karadeniz
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Isothermal Condition ◽  
Strain Energy Function ◽  
Phenomenological Approach ◽  
Elastic Behavior ◽  
Energy Functions ◽  
Strain Energy Functions

Abstract To describe the elastic behavior of rubber-like materials, numerous specific forms of strain energy functions have been proposed in the literature. This bibliography provides a list of references on the strain energy functions for rubber-like materials on isothermal condition using the phenomenological approach. The published works, either containing the strain energy function proposals or the discussions on such proposals, based upon the phenomenological approach, are classified.

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