Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions

2000 ◽  
Vol 123 (3) ◽  
pp. 256-263 ◽  
Author(s):  
Dawn M. Elliott ◽  
Lori A. Setton
Keyword(s):  
Tensile Modulus ◽  
Material Model ◽  
Material Behavior ◽  
Anulus Fibrosus ◽  
Linear Region ◽  
Material Behaviors ◽  
Model Predictions ◽  
Complete Set ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson’s ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4±14.3 MPa versus 5.6±4.7 MPa, outer versus inner sites) and the Poisson’s ratio ν21 (0.67±0.22 versus 1.6±0.7, outer versus inner), but not in the axial modulus (0.8±0.9 MPa) or the Poisson’s ratios ν12 (1.8±1.4) or ν13 (0.6±0.7). These properties were implemented in a linear anisotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for the AF as concentric and physically isolated lamellae may not be appropriate.

Ramberg–Osgood material behavior expression and large deflections of Euler beams

2020 ◽  
pp. 108128652093236
Author(s):  
Ronald J Giardina ◽  
Dongming Wei
Keyword(s):  
Cross Sections ◽  
Nonlinear Behavior ◽  
Material Model ◽  
Material Behavior ◽  
Combined Loading ◽  
Elastic Behavior ◽  
Large Deflections ◽  
Euler Beam ◽  
Special Cases ◽  
Material Behaviors

Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences in the member model response from the true material behavior curve. With the proposed approach, new explicit results for Ramberg–Osgood materials are achieved without relying on these assumptions of material and model expression. The only assumptions present within the proposed model are the standard mechanical assumptions of an Euler beam. A general nonlinear moment–curvature relationship for monotone material behaviors is constructed. Large deflections of cantilever Euler beams with rectangular cross-sections under a combined loading are modeled. Numerical validation of this new method against results already given in the literature for the special cases of linear and power-law material behaviors are provided. An analysis is presented for three common material behavior relationships, with a focus on how these relationships are expressed through the deflection of members under the application of force within the model; this analysis clearly demonstrates that the sub-yield nonlinear behavior of the Ramberg–Osgood expression can be significant. The distinctions between material behavior expression demonstrated in this analysis have been long overlooked within the literature. This work addresses a gap between the modeling of Ramberg–Osgood material behaviors and the implementation of that model in mechanics.

scholarly journals Lamb's problem at its simplest

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120462 ◽  
Author(s):  
Eduardo Kausel
Keyword(s):  
Half Space ◽  
Full Range ◽  
Classical Problem ◽  
Elastic Half Space ◽  
Lamb’S Problem ◽  
Complete Set ◽  
Explicit Formulae ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Single Set

This article revisits the classical problem of horizontal and vertical point loads suddenly applied onto the surface of a homogeneous, elastic half-space, and provides a complete set of exact, explicit formulae which are cast in the most compact format and with the simplest possible structure. The formulae given are valid for the full range of Poisson's ratios from 0 to 0.5, and they treat real and complex poles alike, as a result of which a single set of formulae suffices and also exact formulae for dipoles can be given.

scholarly journals Giant negative Poisson’s ratio in two-dimensional V-shaped materials

2021 ◽  
Author(s):  
Xikui Ma ◽  
Jian Liu ◽  
Yingcai Fan ◽  
Weifeng Li ◽  
Jifan Hu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Two Dimensional ◽  
Auxetic Materials ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

2013 ◽  
Author(s):  
Aaron M. Swedberg ◽  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Large Scale ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Large Strain ◽  
Fiber Direction ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

Carbon nanotube films change Poisson’s ratios from negative to positive

2010 ◽  
Vol 97 (6) ◽  
pp. 061909 ◽  
Author(s):  
Yin Ji Ma ◽  
Xue Feng Yao ◽  
Quan Shui Zheng ◽  
Ya Jun Yin ◽  
Dong Jie Jiang ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Nanotube Films

A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 740-742 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Time Dependence ◽  
Viscoelastic Material ◽  
Lateral Pressure ◽  
Correspondence Principle ◽  
Material Model ◽  
Material Behavior ◽  
Linear Elastic Material ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.

scholarly journals Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

2015 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Abudushalamu Aili ◽  
Matthieu Vandamme ◽  
Jean-Michel Torrenti ◽  
Benoit Masson
Keyword(s):  
Linear Viscoelasticity ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Testing and Simulation of Stress-Stiffening Extreme Poisson’s Ratio Twisted Fiber-Reinforced Elastomer Composites

2008 ◽  
Author(s):  
Larry D. Peel ◽  
Madhuri Lingala
Keyword(s):  
Double Helix ◽  
Fiber Bundles ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Morphing Aircraft ◽  
Active Vibration ◽  
Elastomer Composites ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Twisted Fiber

Laminates that exhibit high and negative Poisson’s ratios can be used as solid-state actuators, passive and active vibration dampers, and for morphing aircraft structures. Recently, fiber-reinforced elastomer (FRE) laminates have been fabricated that exhibit extreme (high and negative) Poisson’s ratios [1]. The current research explores twisted fiber bundle elastomeric laminates (both single and double helix) which are being investigated using experimentation, linear and non-linear finite element analysis (FEA). Twisted fiber bundles can be made from carbon fibers, fiberglass, etc, but for simplicity the current work uses twisted cotton string. It is observed that uniaxial fiber-reinforced elastomer laminates, where the fibers are twisted as shown in Figure 1, exhibit stress stiffening. Negative Poisson’s ratios may be produced if the fiber bundles have a double helical path as simulated by a series of laminated tubes. Future auxetic FRE laminates may be developed that do experience extreme shear.

Hyperelastic Muscle Simulation

2007 ◽  
Vol 345-346 ◽  
pp. 1241-1244 ◽  
Author(s):  
Mohd. Zahid Ansari ◽  
Sang Kyo Lee ◽  
Chong Du Cho
Keyword(s):  
Skeletal Muscle ◽  
Silicone Rubber ◽  
Soft Tissues ◽  
Material Model ◽  
Incompressible Material ◽  
Material Behavior ◽  
Rubber Tube ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior

Biological soft tissues like muscles and cartilages are anisotropic, inhomogeneous, and nearly incompressible. The incompressible material behavior may lead to some difficulties in numerical simulation, such as volumetric locking and solution divergence. Mixed u-P formulations can be used to overcome incompressible material problems. The hyperelastic materials can be used to describe the biological skeletal muscle behavior. In this study, experiments are conducted to obtain the stress-strain behavior of a solid silicone rubber tube. It is used to emulate the skeletal muscle tensile behavior. The stress-strain behavior of silicone is compared with that of muscles. A commercial finite element analysis package ABAQUS is used to simulate the stress-strain behavior of silicone rubber. Results show that mixed u-P formulations with hyperelastic material model can be used to successfully simulate the muscle material behavior. Such an analysis can be used to simulate and analyze other soft tissues that show similar behavior.

scholarly journals Experimental and Numerical Characterization of the Cyclic Thermomechanical Behavior of a High Temperature Forming Tool Alloy

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Sean B. Leen ◽  
Aditya Deshpande ◽  
Thomas H. Hyde
Keyword(s):  
High Temperature ◽  
Life Prediction ◽  
Material Constant ◽  
Superplastic Forming ◽  
Material Model ◽  
Fatigue Tests ◽  
Material Behavior ◽  
Future Application ◽  
Rate Dependent ◽  
Numerical Characterization

This paper describes high temperature cyclic and creep relaxation testing and modeling of a high nickel-chromium material (XN40F) for application to the life prediction of superplastic forming (SPF) tools. An experimental test program to characterize the high temperature cyclic elastic-plastic-creep behavior of the material over a range of temperatures between 20°C and 900°C is described. The objective of the material testing is the development of a high temperature material model for cyclic analyses and life prediction of SPF dies for SPF of titanium aerospace components. A two-layer viscoplasticity model, which combines both creep and combined isotropic-kinematic plasticity, is chosen to represent the material behavior. The process of material constant identification for this model is presented, and the predicted results are compared with the rate-dependent (isothermal) experimental results. The temperature-dependent material model is furthermore applied to simulative thermomechanical fatigue tests, designed to represent the temperature and stress-strain cycling associated with the most damaging phase of the die cycle. The model is shown to give good correlation with the test data, thus vindicating future application of the material model in thermomechanical analyses of SPF dies for distortion and life prediction.

Sign in / Sign up

Export Citation Format

Share Document