Extended Two Compartmental Swelling Stress Model and Isotropic Cauchy Stress Equation for Articular Cartilage Proteoglycans

2007 ◽  
Author(s):  
Sevan R. Oungoulian ◽  
Silvia S. Chen ◽  
Andrew Davol ◽  
Robert L. Sah ◽  
Stephen M. Klisch
Keyword(s):  
Articular Cartilage ◽  
Strain Energy ◽  
Compartmental Model ◽  
Strain Energy Function ◽  
Extended Model ◽  
Cauchy Stress ◽  
Cartilaginous Tissues ◽  
Cartilage Proteoglycans ◽  
Tissue Models ◽  
Total Tissue

Proteoglycans (PGs), a constituent of cartilaginous tissues, have a negative fixed charge (FC) that causes an intratissue swelling stress [1]. This swelling stress is thought to balance tensile stress in the collagen network and contribute to the aggregate modulus of articular cartilage (AC) [1]. Stress constitutive equations that accurately characterize mechanical behavior of individual tissue constituents are crucial for the development of accurate total tissue models. The goal of this study is to extend the range of an existing two compartmental model for PG swelling stress by Basser et al. [1], and develop a continuum level equation for PG Cauchy stress. Specifically, the first aim is to increase the accuracy of the two compartmental model proposed in [1], to a lower range of FC density (FCD) typically found in bovine calf AC. The second aim is to use the extended model to develop a continuum level strain energy function and associated isotropic PG Cauchy stress constitutive equation.

A Novel Approach Towards Modeling the Collagen Fibril Network for Use in Nonlinear Anisotropic Polyconvex Mixture Models of Articular Cartilage

2010 ◽  
Author(s):  
Reza Shirazi ◽  
Pasquale Vena ◽  
Robert L. Sah ◽  
Stephen M. Klisch
Keyword(s):  
Articular Cartilage ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Continuous Distribution ◽  
Strain Energy Function ◽  
Material Point ◽  
Distribution Functions ◽  
Anatomical Location ◽  
Novel Approach

Despite distinct mechanical functions, biological soft tissues have a common microstructure in which a ground matrix is reinforced by a collagen (COL) fibril network. The highly anisotropic, heterogeneous, and asymmetric material properties caused by the microstructural nature of the COL fibril network suggest the importance, as well as the challenges, of accurately modeling soft tissue biomechanics. For soft fibrous tissues with multiple constituents, mathematical distribution functions have represented dispersed and continuous (i.e. non-discrete) fibrils oriented in all directions depending on the type of (and anatomical location in) the tissue under investigation [1–2]. These types of continuous fibril models have been used recently for articular cartilage [3–5]. The strain energy of the COL fibril network is calculated based on the response of individual fibrils in tension in different directions and integrated over a unit sphere at a material point. The specific aims of the current study were to: 1. introduce a novel approach to modeling a continuous distribution of COL fibrils in soft tissues; 2. develop a strain energy function for the COL network based on the proposed distribution function of COL fibrils; 3. derive the stress and material elasticity tensors for the COL network that may be “pre-stressed” in a stress-free natural configuration of the tissue; 4. propose a special model that may be appropriate for immature tissue and establish its suitability for use in a polyconvex tissue strain energy function.

A REVIEW OF THE MECHANICAL STRESSES PREDISPOSING ABDOMINAL AORTIC ANEURYSMAL RUPTURE: UNIAXIAL EXPERIMENTAL APPROACH

2020 ◽  
Vol 20 (08) ◽  
pp. 2030001
Author(s):  
MARIYA ANTONOVA ◽  
SOFIA ANTONOVA ◽  
LYUDMILA SHIKOVA ◽  
MARIA KANEVA ◽  
VALENTIN GOVEDARSKI ◽  
...  
Keyword(s):  
Strain Energy ◽  
Experimental Approach ◽  
Strain Energy Function ◽  
Ultimate Stress ◽  
Physical Parameters ◽  
Stress And Strain ◽  
Cauchy Stress ◽  
Biomechanical Behavior ◽  
Abdominal Aortic ◽  
Experimental Protocols

In this paper, problems concerning the uniaxial experimental investigation of the human abdominal aortic aneurysm (AAA) biomechanical characteristics, concomitant values of the associated Cauchy stress, failure (ultimate) stress in AAA, and the constitutive modeling of AAA are considered. The aim of this paper is to review and compare the disposable experimental data, to reveal the reasons for the high dissipation of the results between studies, and to propound some unification criteria. We examined 22 literature sources published between 1994 and 2017 and compared their results, including our own results. The experiments in the reviewed literature have been designed to obtain the stress–strain characteristics and the failure (ultimate) stress and strain of the aneurysmal tissue. A variety of forms of the strain–energy function (SEF) have been applied in the considered studies to model the biomechanical behavior of the aneurysmal wall. The specimen condition and physical parameters, the experimental protocols, the failure stress and strain, and SEFs differ between studies, contributing to the differences between the final results. We propound some criteria and suggestions for the unification of the experiments leading to the comparable results.

scholarly journals A Bimodular Polyconvex Anisotropic Strain Energy Function for Articular Cartilage

2006 ◽  
Vol 129 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Stephen M. Klisch
Keyword(s):  
Articular Cartilage ◽  
Strong Interaction ◽  
Energy Function ◽  
Strain Energy ◽  
Mechanical Response ◽  
Deformation Gradient ◽  
Strain Energy Function ◽  
Finite Deformations ◽  
Orthotropic Materials ◽  
Interaction Terms

A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex “strong interaction terms” for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson’s ratios, as well as axial stress–axial strain responses, in tension and compression for finite deformations.

Mechanical power and hyperelasticity

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Power ◽  
Elastic Materials ◽  
Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Mechanical characterization of a woven multi-layered hyperelastic composite laminate under uniaxial loading

2021 ◽  
pp. 002199832110115
Author(s):  
Shaikbepari Mohmmed Khajamoinuddin ◽  
Aritra Chatterjee ◽  
MR Bhat ◽  
Dineshkumar Harursampath ◽  
Namrata Gundiah
Keyword(s):  
Composite Materials ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Mechanical Tests ◽  
Stress Strain ◽  
Aerospace Applications ◽  
Envelope Material ◽  
The Individual ◽  
High Dielectric

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

Bifurcation of rotating circular cylindrical elastic membranes

1980 ◽  
Vol 87 (2) ◽  
pp. 357-376 ◽  
Author(s):  
D. M. Haughton ◽  
R. W. Ogden
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Strain Energy Function ◽  
Angular Speed ◽  
Elastic Membrane ◽  
Axial Extension ◽  
End Conditions ◽  
Elastic Membranes ◽  
Realistic Choice

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.

Sign in / Sign up

Export Citation Format

Share Document