Phenomenological Hyperelastic Strain-Stiffening Constitutive Models for Rubber

2006 ◽  
Vol 79 (1) ◽  
pp. 152-169 ◽  
Author(s):  
Cornelius O. Horgan ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problems ◽  
Soft Tissues ◽  
Boundary Value ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Large Strains ◽  
Shear Mode ◽  
Crack Problems ◽  
Gent Model ◽  
Constitutive Parameters

Abstract Many rubber-like materials and soft biological tissues exhibit a significant stiffening or hardening in their stress-strain curves at large strains. The accurate modeling of this phenomenon is a key issue for a better understanding of the thermomechanics of rubber and the biomechanics of soft tissues. In this paper, we provide a review of some phenomenological hyperelastic constitutive models that have been proposed to model this strain stiffening effect and summarize recent advances in the solution of boundary-value problems that illustrate the utility of such models. The emphasis is on constitutive models that reflect limiting chain extensibility at the molecular level. A remarkably simple phenomenological model of this type has been proposed by Gent. The Gent model has a molecular basis related to the inverse Langevin function compact support non-Gaussian statistics for the end-to-end distance function. The mathematical simplicity of the Gent model, which contains just two constitutive parameters, has facilitated the analytic solution of a variety of specific boundary-value problems that are relevant to the rubber industry and we summarize the main results here. These problems include those of torsion, axial, azimuthal and helical shear, anti-plane shear, mode III crack problems, rotation induced deformation of circular cylinders and fracture problems. It is shown that the results are radically different from those obtained in the literature for classical models such as the neo-Hookean and Mooney-Rivlin models for incompressible rubber. Extensions to include thermoelasticity, material compressibility, anisotropy and stress softening are also briefly described.

A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Franz G. Sander ◽  
Christina Dorow ◽  
...  
Keyword(s):  
Strain Rate ◽  
Periodontal Ligament ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Experimental Testing ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Time Dependent ◽  
Large Strains ◽  
Free Energy Function

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Constitutive Formulation for Numerical Analysis of Visco-Hyperelastic Damage Phenomena in Soft Biological Tissues

2006 ◽  
Author(s):  
Arturo N. Natali ◽  
Emanuele L. Carniel ◽  
Piero G. Pavan ◽  
Alessio Gasparetto ◽  
Franz G. Sander ◽  
...  
Keyword(s):  
Strain Rate ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Experimental Tests ◽  
Biological Tissues ◽  
Tissue Response ◽  
Time Dependent ◽  
Soft Biological Tissues ◽  
Constitutive Formulation

Soft biological tissues show a strongly non linear and time-dependent mechanical response and undergo large strains under physiological loads. The microstructural arrangement determines specific anisotropic macroscopic properties that must be considered within a constitutive formulation. The characterization of the mechanical behaviour of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non linearity. In the model presented here a hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for soft tissues and can be properly arranged for the investigation of viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. This phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. This makes it possible to perform numerical analyses of the mechanical response considering time-dependent effects and damage phenomena. The experimental tests develop investigated tissue response for different strain rate conditions, accounting for stretch situations capable of inducing damage phenomena. The reliability of the formulation is evaluated by a comparison with the results of experimental tests performed on pig periodontal ligament.

scholarly journals Boundary Value Problems of Potential Functions in Decagonal Quasicrystals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wu Li ◽  
Hao Xin ◽  
Tianyou Fan
Keyword(s):  
Boundary Value Problems ◽  
Edge Crack ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Potential Functions ◽  
Crack Model ◽  
Finite Width ◽  
Single Edge ◽  
Decagonal Quasicrystals ◽  
Crack Problems

A unified form of potential functions in decagonal quasicrystals (QCs) and conformal mappings are applied in a novel way to solve the boundary value problems emanating from the generalized theory of elasticity for decagonal QCs. By executing the reduction of boundary value problem to function equations, two crack problems are investigated. In the first one, an approximate analysis for bending specimen with a crack is given. In the other, a finite width strip with single edge crack of decagonal QCs is analytically estimated. Using the basic idea underlying Dugdale’s crack model, the extent of cohesive force zone in each of the two cases is analytically derived.

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

2015 ◽  
Vol 60 (6) ◽  
Author(s):  
Cora Wex ◽  
Susann Arndt ◽  
Anke Stoll ◽  
Christiane Bruns ◽  
Yuliya Kupriyanova
Keyword(s):  
Mechanical Behaviour ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Tissue Response ◽  
Large Strains ◽  
Energy Functions ◽  
Strain Energy Functions ◽  
Hyperelastic Models

AbstractModelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function – a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Optimal Constitutive Parameters and Subject Specific Variability: An Application to the Aortic Sinuses

2013 ◽  
Author(s):  
Vittoria Flamini ◽  
Boyce E. Griffith
Keyword(s):  
Constitutive Models ◽  
Biological Tissues ◽  
Mechanical Tests ◽  
Tissue Samples ◽  
Subject Specific ◽  
Mechanical Models ◽  
Outlier Tests ◽  
Definition Of ◽  
Computational Analyses ◽  
Constitutive Parameters

Advanced analyses of soft biological tissues have shown substantial subject-specific variability in mechanical properties [1]. Such variability is also easily observed at a geometrical or morphological level, and has been reported also in mechanical tests on biological tissue samples [1, 2]. While there is wide interest in reproducing accurate geometries for subject-specific modeling, constitutive parameters for mechanical models often use averaged data from mechanical tests [3]. Outliers are typically neglected, and only the ‘mean’ tissue behavior is considered. However, due to an increased interest in using multi-scale and finite element (FE) models for medical device testing and surgical planning [4], understanding of the variability of the outlier tests becomes increasingly important. In particular, by using detailed mechanistic constitutive models, it might be possible to classify the different mechanical behaviors observed on the basis of the changes in the constitutive parameters. This process could lead to the definition of a library of different ‘healthy’ or ‘diseased’ constitutive parameters to be used in computational analyses.

Rapid Critical Point Drying of Tissues in a Parr Bomb

1972 ◽  
Vol 30 ◽  
pp. 400-401
Author(s):  
C.A. Baechler ◽  
W. C. Pitchford ◽  
J. M. Riddle ◽  
C.B. Boyd ◽  
H. Kanagawa ◽  
...  
Keyword(s):  
Critical Point ◽  
Critical Pressure ◽  
Soft Tissues ◽  
Biological Tissues ◽  
Critical Temperatures ◽  
Air Drying ◽  
The Past ◽  
Critical Point Drying ◽  
Great Stress ◽  
Infiltration Techniques

Preservation of the topographic ultrastructure of soft biological tissues for examination by scanning electron microscopy has been accomplished in the past by using lengthy epoxy infiltration techniques, or dehydration in ethanol or acetone followed by air drying. Since the former technique requires several days of preparation and the latter technique subjects the tissues to great stress during the phase change encountered during air-drying, an alternate rapid, economical, and reliable method of surface structure preservation was developed. Turnbill and Philpott had used a fluorocarbon for the critical point drying of soft tissues and indicated the advantages of working with fluids having both moderately low critical pressures as well as low critical temperatures. Freon-116 (duPont) which has a critical temperature of 19. 7 C and a critical pressure of 432 psi was used in this study.

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