Large Deformation Mechanics of the Enucleated Eyeball

1984 ◽  
Vol 106 (3) ◽  
pp. 229-234 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Large Deformation ◽  
Strain Energy Function ◽  
Membrane Action ◽  
Filled Rubber ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Deformation Mechanics ◽  
Type Of Failure ◽  
Energy Formulation ◽  
Good Agreement

Large deformation of enucleated pig eyeballs under rigid cylindrical indenters was studied analytically and experimentally. The analytic model for the eyeball consists of a fluid-filled spherical membrane composed of an incompressible, elastic material with an exponential strain energy function. The Rayleigh-Ritz technique provided an approximate solution via a potential energy formulation. Comparison with results from tests on eyeballs and a water-filled rubber (Mooney-Rivlin) shell shows good agreement at large deflection, where membrane action dominates. Due to the highly nonlinear stress-strain relations for the sclera, the load remains relatively small until the indenter displacement approaches 40–60 percent of the eyeball radius, and then the load increases rapidly. Depending on the indenter size, either a perforation or a rupture type of failure occurs.

scholarly journals Effects of Large Deformation and Velocity Impacts on the Mechanical Behavior of Filled Rubber: Microstructure-Based Constitutive Modeling and Mechanical Testing

Polymers ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2322
Author(s):  
Wei Wei ◽  
Yong Yuan ◽  
Xiaoyu Gao
Keyword(s):  
Mechanical Behavior ◽  
Large Deformation ◽  
Energy Function ◽  
Constitutive Modeling ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Shear Loading ◽  
Stress Strain ◽  
Cyclic Shear ◽  
Filled Rubber

Filled rubber has been extensively used in the repairing, retrofitting, and protecting of civil infrastructures due to its superior physical and mechanical properties. However, effects of large deformation and velocity impacts on the mechanical behavior of filled rubber are not well recognized, one of the major challenges in the past investigations is that the material exhibits significant nonlinearity and sensitivity to velocity. This paper presents a hyper-viscoelastic constitutive modeling and experimental study to capture both the hyperelastic and viscoelastic behaviors of filled rubber under large shear deformation and velocity impacts. Motivated by the micro-mechanism of filled rubber, the constitutive modeling consists of an equilibrium element in parallel with an improved Maxwell element to incorporate both nonlinear hyperelasticity and rate-dependent performance governed by the readjustment and rearrangement of molecular chains in the material. A new strain energy function is developed and the physical description of parameters in the strain energy function is highlighted. The Clausius-Duhem inequality is employed to consider the thermodynamic consistency of the model. Then, stress relaxation property and stress-strain response of filled rubber upon cyclic shear loading with different strain rates (ranging from 0.08 to 12.0 s−1) are experimentally studied, and some key observations are summarized. Subsequently, a “Gau-Poly” function is proposed based on the experimental data to describe the viscoelastic property of filled rubber versus strain and strain rate. Finally, stress-strain relationship and hysteretic area obtained from the experimental results were compared with the numerical results of the model, good agreement was achieved and the capacity of the model to accurately reproduce the mechanical behavior of filled rubber under a wide range of deformation and velocity impacts was verified.

Inversion of a Class of Nonlinear Stress-Strain Relationships of Biological Soft Tissues

1979 ◽  
Vol 101 (1) ◽  
pp. 23-27 ◽  
Author(s):  
Y. C. Fung
Keyword(s):  
Stress Tensor ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Tensor ◽  
Nonlinear Function ◽  
Strain Energy Function ◽  
Stress Strain ◽  
Highly Nonlinear ◽  
Nonlinear Stress

The mechanical properly of soft tissues is highly nonlinear. Normally, the stress tensor is a nonlinear function of the strain tensor. Correspondingly, the strain energy function is not a quadratic function of the strain. The problem resolved in the present paper is to invert the stress-strain relationship so that the strain tensor can be expressed as a nonlinear function of the stress tensor. Correspondingly, the strain energy function is inverted into the complementary energy function which is a function of stresses. It is shown that these inversions can be done quite simply if the strain energy function is an analytic function of a polynomial of the strain components of the second degree. We have shown previously that experimental results on the skin, the blood vessels, the mesentery, and the lung tissue can be best described by strain energy functions of this type. Therefore, the inversion presented here is applicable to these tissues. On the other hand, a popular strain energy function, a polynomial of third degree or higher, cannot be so inverted.

scholarly journals Mechanical Testing and Modeling of the Time–Temperature Superposition Response in Hybrid Fiber Reinforced Composites

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1178
Author(s):  
Aggelos Koutsomichalis ◽  
Thomas Kalampoukas ◽  
Dionysios E. Mouzakis
Keyword(s):  
Hybrid Composites ◽  
High Stress ◽  
Woven Fabrics ◽  
Mathematical Function ◽  
Ballistic Performance ◽  
Three Point Bending ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Temperature Superposition ◽  
Time Temperature Superposition

The purpose of this study was to manufacture hybrid composites from fabrics with superior ballistic performance, and to analyze their viscoelastic and mechanical response. Therefore, composites in hybrid lay-up modes were manufactured from Vectran, Kevlar and aluminum fiber-woven fabrics through a vacuum assisted resin transfer molding. The specimens were consequently analyzed using static three-point bending, as well as by dynamic mechanical analysis (DMA). Apart from DMA, time–temperature superposition (TTS) analysis was performed by all available models. It was possible to study the intrinsic viscoelastic behavior of hybrid ballistic laminates, with TTS analysis gained from creep testing. A polynomic mathematical function was proposed to provide a high accuracy for TTS curves, when shifting out of the linearity regimes is required. The usual Williams–Landel–Ferry and Arrhenius models proved not useful in order to describe and model the shift factors of the acquired curves. In terms of static results, the highly nonlinear stress–strain curve of both composites was obvious, whereas the differential mechanism of failure in relation to stress absorption, at each stage of deformation, was studied. SEM fractography revealed that hybrid specimens with Kevlar plies are prone to tensile side failure, whereas the hybrid specimens with Vectran plies exhibited high performance on the tensile side of the specimens in three-point bending, leading to compressive failure owing to the high stress retained at higher strains after the maximum bending strength was reached.

scholarly journals Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1223
Author(s):  
Elisa Ficarella ◽  
Mohammad Minooei ◽  
Lorenzo Santoro ◽  
Elisabetta Toma ◽  
Bartolomeo Trentadue ◽  
...  
Keyword(s):  
Zona Pellucida ◽  
Soft Matter ◽  
Mechanical Response ◽  
Mechanical Characterization ◽  
Nonlinear Material ◽  
Prony Series ◽  
Critical Comparison ◽  
Highly Nonlinear ◽  
Good Agreement

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda–Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP’s mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force–indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

scholarly journals Design analysis of four-wave-mixing in SiN nanowires integrated with graphene oxide films

2020 ◽  
Author(s):  
David Moss
Keyword(s):  
Graphene Oxide ◽  
Kerr Nonlinearity ◽  
Four Wave Mixing ◽  
Wave Mixing ◽  
Trade Off ◽  
Material Parameters ◽  
Highly Nonlinear ◽  
Thermal Changes ◽  
Strong Mode ◽  
Good Agreement

<p>We theoretically investigate and optimize four-wave mixing (FWM) in silicon nitride (SiN) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. Based on extensive previous measurements of the material parameters of the GO films, we perform detailed analysis for the influence of device parameters including waveguide geometry, GO film thickness, length, and coating position on the FWM conversion efficiency (CE) and conversion bandwidth (CB). The influence of dispersion and photo-thermal changes in the GO films is also discussed. Owing to the strong mode overlap between the SiN waveguides and the highly nonlinear GO films, FWM in the hybrid waveguides can be significantly enhanced. We obtain good agreement with previous experimental results and show that by optimizing the device parameters to balance the trade-off between Kerr nonlinearity and loss, the FWM CE can be improved by as much as ~20.7 dB and the FWM CB can be increased by ~4.4 folds, relative to the uncoated waveguides. These results highlight the significantly enhanced FWM performance that can be achieved in SiN waveguides by integrating 2D layered GO films.<i></i></p>

Biaxial mechanical behavior of excised ventricular epicardium

1990 ◽  
Vol 259 (1) ◽  
pp. H101-H108 ◽  
Author(s):  
J. D. Humphrey ◽  
R. K. Strumpf ◽  
F. C. Yin
Keyword(s):  
Mechanical Behavior ◽  
Cardiac Mechanics ◽  
Left Ventricular ◽  
Biaxial Stress ◽  
Biomechanical Behavior ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Parietal Pericardium ◽  
The Right

We present results from in vitro biaxial stress-strain experiments on epicardium excised from the right and left ventricular free walls of canine hearts. These data reveal that the biomechanical behavior of ventricular epicardium is qualitatively similar to atrial epicardium and parietal pericardium but different from noncontracting myocardium. In particular, ventricular epicardium exhibits a highly nonlinear stress-stretch behavior, being initially compliant but then very stiff near the limits of its extensibility. In addition, the epicardium appears to be initially isotropic but becomes markedly anisotropic upon rapid stiffening. Finally, specimens taken from the right and left ventricular free walls behaved similarly. We submit that excised ventricular epicardium is capable of carrying significant in-plane loads and that there is a need to investigate further its role in local and global cardiac mechanics and physiology.

scholarly journals Bioengineering. Large Deformation Mechanics of Plasma Membrane Chained Vesicles in Cells.

2001 ◽  
Vol 44 (4) ◽  
pp. 928-936 ◽  
Author(s):  
Tadashi KOSAWADA ◽  
Kouichi SANADA ◽  
Tetsuo TAKANO
Keyword(s):  
Plasma Membrane ◽  
Large Deformation ◽  
Deformation Mechanics ◽  
In Cells

scholarly journals DEVELOPMENT OF OPEN SOURCE FINITE ELEMENT SOLVER “LD-FEM’ FOR MODELING AND SIMULATION OF RUBBER MATERIALS

ROTASI ◽  
2014 ◽  
Vol 16 (3) ◽  
pp. 10
Author(s):  
Sugeng Waluyo
Keyword(s):  
Finite Element ◽  
Open Source ◽  
Large Deformation ◽  
Strain Energy ◽  
Nonlinear Behavior ◽  
Strain Energy Function ◽  
Numerical Approach ◽  
Uniaxial Tensile ◽  
Material Stiffness ◽  
Loading Tests

“LD-FEM” is an open source computer program working on the basis of finite element method (FEM) which is aimed to model and simulate large deformation in rubber materials. The kinematics of large deformation on the basis of the Total Lagrange framework is applied to linear 4-nodes tetrahedral element and then solved with Newton-Raphson iterative scheme. Furthermore, to obtain the material tangent stiffness directly from strain energy density functions, the Gill-Murray theory of numerical second derivative is used in LD-FEM. Finally, by using the Mooney-Rivlin strain energy function, the performance of LD-FEM is addressed for uniaxial tensile, shear and torsion loading tests. The results confirm the capability of LD-FEM to capture nonlinear behavior of the large deformation either with analytical or numerical approach on the material stiffness derivation with error less than 2%.

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