Composite Structure Design of O-Rings Using Material Behavior to Decrease Strain Energy and Permanent Deformation

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Nicholas J. Maciejewski ◽  
Ryan B. Sefkow ◽  
Barney E. Klamecki
Keyword(s):  
Strain Energy Density ◽  
Strain Energy ◽  
Energy Content ◽  
Permanent Deformation ◽  
Material Behavior ◽  
Finite Element Models ◽  
Stress Strain ◽  
Strain Behavior ◽  
Ring Section ◽  
Over Time

The performance of elastomeric seals degrades over time in use due to the development of permanent material deformation. The existence of localized high stress regions below seal-housing contact areas led to consideration of improving O-ring design by modifying material behavior to decrease strain energy, and so permanent deformation, in these regions. Photoelastic stress analysis was used to experimentally characterize the stress and strain fields in O-ring sections and to validate finite element models used in design studies. O-ring section designs that included small inset regions of different material behavior than the larger surrounding section were investigated with the intent of manipulating and reducing the strain energy content. Finite element models of O-rings were used to characterize the strain energy content and distribution for inset materials with various stress-strain behaviors. Measurements of permanent deformation and load-deflection behavior of specimens held under applied compression over time showed dependence of the amount of permanent deformation on strain energy. Design rules were extracted from results of studies in which inset region material stiffness, stress-strain behavior, size, and location in the larger section were varied. O-ring sections with regions of less stiff material result in lower strain energy and more uniform strain energy density distribution than the typical one-material seal. Inclusion of less stiff softening stress-strain behavior material insets in the larger O-ring section produced reduction in strain energy level and favorable redistribution of the high strain energy density regions compared with the conventional one-material one-material-behavior design. Similar concepts will apply to the design of other elastomeric structures in which permanent material deformation affects structure performance.

Contribution to the Mathematical Description of Stress-Strain Behavior of Elastomers

1980 ◽  
Vol 53 (4) ◽  
pp. 836-841 ◽  
Author(s):  
K. Tobisch
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Mathematical Description ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Pure Shear ◽  
Simple Extension ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Energy Density Function

Abstract Based on the hypothesis of Valanis and Landel that the strain energy density function W(λx,λy,λz)could be represented as the sum of three identical functions ω(λi) of the principal extension ratios λi(i=x,y,z), an expression for ω(λi) is suggested which is distinguished by its relative simplicity. The stress-strain relations developed from this expression are tested successfully by applying them to experimental results of other authors. The types of strain which were examined were simple extension, biaxial extension and pure shear; the elongations were to about 700%.

Improving the Long-Term Performance of Elastomeric Seals by Material Behavior Design

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Ryan B. Sefkow ◽  
Nicholas J. Maciejewski ◽  
Barney E. Klamecki
Keyword(s):  
Energy Density ◽  
Contact Pressure ◽  
Strain Energy ◽  
Applied Pressure ◽  
Material Behavior ◽  
Time Dependent ◽  
Ring Section ◽  
Stiff Material ◽  
Elastomeric Seals

Previously it was shown that including smaller inset regions of less stiff material in the larger O-ring section at locations of high stress results in lower strain energy density in the section. This lower energy content is expected to lead to improved long-term seal performance due to less permanent material deformation and so less loss of seal-housing contact pressure. The shape of the inset region, the time-dependent change in material properties, and hence change in seal behavior over time in use were not considered. In this research experimental and numerical simulation studies were conducted to characterize the time-dependent performance of O-ring section designs with small inset regions of different mechanical behaviors than the larger surrounding section. Seal performance in terms of the rate of loss of contact pressure of modified designs and a baseline elastic, one-material design was calculated in finite element models using experimentally measured time-dependent material behavior. The elastic strain energy fields in O-ring sections were calculated under applied pressure and applied displacement loadings. The highest stress, strain, and strain energy regions in O-rings are near seal-gland surface contacts with significantly lower stress in regions of applied pressure. If the size of the modified region of the seal is comparable to the size of the highest energy density region, the shape of the inset is not a major factor in determining overall seal section behavior. The rate of loss of seal-housing contact pressure over time was less for the modified design O-ring sections compared with the baseline seal design. The time-dependent performance of elastomeric seals can be improved by designing seals based on variation of mechanical behavior of the seal over the seal section. Improvement in retention of sealing contact pressure is expected for seal designs with less stiff material in regions of high strain energy density.

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.

Fatigue Life Law Based on Inelastic Strain Energy Density of Solder Alloys and its Simple Prediction Method

2020 ◽  
Author(s):  
Tomoya Fumikura ◽  
Mitsuaki Kato ◽  
Takahiro Omori
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Test ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Prediction Method ◽  
Strain Range ◽  
Inelastic Strain ◽  
Stress Strain ◽  
Wide Range

Abstract In recent years, a fatigue life law based on inelastic strain energy density as proposed by Morrow has been applied to solder materials. In this study, the effectiveness of the fatigue life law based on inelastic strain energy density was compared with the conventional law based on inelastic strain range. First, the fatigue properties of Sn-Ag-Cu solder alloy were investigated by a torsional fatigue test with strain control. It was found that the stress–strain hysteresis loop arising from inelastic deformation occurred even under a low strain load with a fatigue life of about 1 million cycles. Therefore, as an extension of the low-cycle fatigue test, evaluation was performed using inelastic strain range and inelastic strain energy density. Experimental results show that when fatigue life was evaluated using inelastic strain energy density, a single power law was found over a wide range from the low-cycle region to the high-cycle region, and the validity of the fatigue life law based on inelastic strain energy density was confirmed. Next, a simple prediction method for the fatigue life law based on inelastic strain energy density was examined, taking the physical background into account. Two material constants of the fatigue life law based on the inelastic strain energy density were estimated from the stress–strain curve for a monotonic load and shown to be close to the actual fatigue test results.

scholarly journals Influence of the Temporomandibular Joint in the Estimation of Bone Density in the Mandible through a Bone Remodelling Model

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Maria S. Commisso ◽  
Joaquín Ojeda ◽  
Juana Mayo ◽  
Javier Martínez-Reina
Keyword(s):  
Bone Density ◽  
Temporomandibular Joint ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Bone Remodelling ◽  
Realistic Model ◽  
Mechanical Stimulus ◽  
Finite Element Models ◽  
Articular Disc ◽  
Detailed Model

The temporomandibular joint (TMJ) plays a key role in the distribution of stresses in the mandible during mastication and consequently in the distribution of bone density, due to the interconnection between both variables through bone remodelling. Two finite element models of the mandible were compared to study the influence of the redistribution of stresses produced by the joint: (1) a model without TMJ, but with simplified boundary conditions to replace the joint, as done in previous models; (2) a more realistic model including the articular disc and some ligaments present in the TMJ. The stresses and strains in both models were compared through the strain energy density, used in many bone remodelling models as a measure of the mechanical stimulus. An anisotropic bone remodelling model was used to simulate the behaviour of mandible bone and to estimate its density distribution. The results showed that the TMJ strongly affects the stress distribution, the mechanical stimulus, and eventually the bone density, and not only locally in the condyle, but also in the whole mandible. It is concluded that it is utterly important to include a detailed model of the TMJ to estimate more correctly the stresses in the mandible during mastication and, from them, the bone density and anisotropy distribution.

On the Small Strain Behavior of Peroxide Crosslinked Natural Rubber

1986 ◽  
Vol 59 (1) ◽  
pp. 130-137 ◽  
Author(s):  
Gregory B. McKenna ◽  
Louis J. Zapas
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Scaling Law ◽  
Small Strain ◽  
Constant Length ◽  
Strain Behavior ◽  
Small Strains ◽  
Strain Energy Density Function

Abstract Torque and normal force measurements on a cylinder subjected to torsion at constant length were used to study the behavior of NR crosslinked with 5 phr dicumyl peroxide. The derivatives of the strain-energy density function ∂W/∂I1 and ∂W/∂I2 were calculated from the data using the scaling law of Penn and Kearsley. The new results extend the limit of small strains at which the strain-energy density function derivatives have been measured to γ<0.005 and further confirm our previous results that for peroxide-crosslinked NR, ∂W/∂I2 does not become negative at small strain, contrary to several reports in the literature. Reduced stress was determined for the rubber by using the approach of Kearsley and Zapas to calculate the derivative w′(λ) of the Valanis-Landel form of the strain energy function. The results were compared with the measured values for reduced stress in tension and compression at small strains. While the deviation between the predictions and the experimental behavior do not exceed 6%, the characters of the calculated and measured reduced stress plots are different. The measurements in torsion were not obtained at small enough strains to enable direct comparison with the extension/compression behavior at |ε|<0.002. Extrapolation of the results did not produce the anomalous cusp observed in the reduced stress for 0.998<1/λ<1.002 which was reported in our previous study. The fact that torsional data do not show the cusp offers support to the Kearsley suggestion that at these extremely small deformations, rubber compressibility may play an important role in the stress-strain behavior. This could also explain the apparent discrepancy between the predicted Valanis-Landel behavior and the observed behavior. Future work involving higher precision experiments is required to resolve the matter.

Probabilistic Structural Analysis for Advanced Space Propulsion Systems

1990 ◽  
Vol 112 (2) ◽  
pp. 251-260 ◽  
Author(s):  
T. A. Cruse ◽  
J. F. Unruh ◽  
Y.-T. Wu ◽  
S. V. Harren
Keyword(s):  
Structural Analysis ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Significant Advance ◽  
Space Propulsion ◽  
Stress Strain ◽  
Ongoing Research ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Random Material Properties

This paper reports on recent extensions to ongoing research into probabilistic structural analysis modeling of advanced space propulsion system hardware. The advances concern probabilistic dynamic loading, and probabilistic nonlinear material behavior. In both cases, the reported work represents a significant advance in the state-of-the-art for these topics. Random, or probabilistic loading is normally concerned with the loading described in power spectral density (PSD) terms. The current work describes a method for incorporating random PSD’s along with random material properties, damping, and structural geometry. The probabilistic material response is concerned with the prediction of nonlinear stress-strain behavior for physical processes that can be linked to the original microstructure of the material. Such variables as grain size and orientation, grain boundary strength, etc., are treated as random, initial variables in generating stochastic stress-strain curves. The methodology is demonstrated for a creep simulation.

scholarly journals Strain Energy Density as Failure Criterion for Quasi-Static Uni-axial Tensile Loading

2021 ◽  
Vol 15 (57) ◽  
pp. 331-349
Author(s):  
Andrea Kusch ◽  
Simone Salamina ◽  
Daniele Crivelli ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Tensile Load ◽  
Strain Curve ◽  
Material Behavior ◽  
Uniaxial Tensile ◽  
Notched Specimens ◽  
Nonlinear Stress

Strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. This work investigates the possibility to use this method to predict the strength of V-notched specimens made of PMMA under static uniaxial tensile load. Samples are characterized by a variability of notch root radii and notch opening angles. Notched specimens fail with a quasi-brittle behavior, albeit PMMA has a nonlinear stress strain curve at room temperature. The notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. The value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. Failure prediction, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data.

Characterization of Stress-Strain Behavior of Superplastic Titanium Alloy by Free Bulging Tests with Pressure Jumps

2018 ◽  
Vol 385 ◽  
pp. 443-448 ◽  
Author(s):  
Sergey A. Aksenov ◽  
Donato Sorgente
Keyword(s):  
Strain Rate ◽  
Material Model ◽  
Material Behavior ◽  
Dome Height ◽  
Sensitivity Index ◽  
Stress Strain ◽  
Strain Behavior ◽  
Direct Technique ◽  
Pressure Regime ◽  
Free Bulging

The work is dedicated to determination of stress-strain behavior of Ti6Al4V alloy deformed in conditions of biaxial tension provided by free bulging testing. The dome height during each test was continuously measured and recorded using a magnetostrictive position transducer. All the tests were performed using stepped pressure regime with jump pressure changing between two values at evenly spaced time moments. This experimental technique provides the possibility to study strain rate sensitivity index variation during the test and subsequently construct strain and strain rate dependent material model. The output data of each test include the evolution of dome height, subsequent pressure regime and final thickness of the specimen at the dome pole. In the framework of this study the processing of such data in order to evaluate the material behavior is discussed. Inverse analysis with different material models was implemented as well as special direct technique allowing one to construct stress-strain curves based on the results of free bulging tests with pressure jumps. The obtained material model was verified by finite element simulation.

Adaptation of a Rabbit Myocardium Material Model for Use in a Canine Left Ventricle Simulation Study

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Matthew G. Doyle ◽  
Stavros Tavoularis ◽  
Yves Bourgault
Keyword(s):  
Left Ventricle ◽  
Material Parameter ◽  
Muscle Fibers ◽  
Active Material ◽  
Material Model ◽  
Material Behavior ◽  
Stress Strain ◽  
Stress Measurements ◽  
Strain Behavior ◽  
Parameter Values

The myocardium of the left ventricle (LV) of the heart comprises layers of muscle fibers whose orientation varies through the heart wall. Because of these fibers, accurate modeling of the myocardium stress-strain behavior requires models that are nonlinear, anisotropic, and time-varying. This article describes the development and testing of a material model of the canine LV myocardium, which will be used in ongoing simulations of the mechanics of the LV with fluid-structure interaction. The model assumes that myocardium deformation has two extreme states: one during which the muscle fibers are fully relaxed, and another during which the muscle fibers are fully contracted. During the second state, the “total” stresses are assumed to be the sum of “passive” stresses, which represent the fully relaxed muscle fibers, and “active” stresses, which are additional stresses due to the contraction of the muscle fibers. The canine LV myocardium is modeled as a transversely isotropic material for which material properties vary in the fiber and cross-fiber directions. The material behavior is considered to be hyperelastic and is modeled by a strain-energy density function in a manner that is an adaptation of an approach based on measurements of the stress-strain behavior of rabbit LV myocardia. A numerical method has been developed to calculate suitable parameter values for the passive material model using previous passive canine LV myocardium stress measurements and taking into account existing physical and numerical constraints. In the absence of published measurements of total canine LV myocardium stresses, a method has been developed to estimate these stresses from available passive and total rabbit LV myocardium stresses and then to calculate active material parameter values. Material parameter values were calculated for passive and active canine LV myocardium. Passive stresses calculated using the model compare well to previous stress measurements while active stresses calculated using the model compare well with those approximated from rabbit measurements. The adapted material model of the canine LV myocardium is deemed to be suitable for use in simulations of the operation of both idealized and realistic canine hearts. The estimated model parameter values can be easily revised to more appropriate ones if measurements of active canine LV myocardium stresses become available. The extension of this material model to a fully orthotropic one is also possible but determination of its parameters would require stress-stretch measurements in the fiber and both cross-fiber directions.

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