ENTIRE-REGION CONSTITUTIVE RELATION FOR TRELOAR'S DATA

2021 ◽  
Author(s):  
L. Han ◽  
X. F. Peng ◽  
L. X. Li
Keyword(s):  
Experimental Data ◽  
Constitutive Relation ◽  
Large Deformations ◽  
Constitutive Relations ◽  
Entire Region ◽  
Energy Functions ◽  
Practical Applications ◽  
Hyperelastic Materials ◽  
Present Procedure ◽  
Modeling Theory

ABSTRACT Hyperelastic materials can experience a large deformation process. A constitutive relation suitable for an entire region from small, moderate, to large deformations is of great importance for practical applications such as fracture problems. Treloar's data are first investigated, and the tension curve is divided into three regimes: small-to-moderate regime, strain-hardening regime, and limiting-chain regime. Next, the modeling theory of hyperelastic materials is introduced, and the tensile behaviors of basic energy functions are analyzed for different deformation regimes. Finally, a successive procedure is suggested to establish an entire-region constitutive relation and then applied to Treloar's data. The present constitutive relation can maintain the initial shear modulus while the experimental data are satisfactorily predicted. The present procedure is simple and feasible and hence applicable to other hyperelastic materials when their entire-region constitutive relations are studied based on experimental data.

Constitutive Relations of Masonry under Compression — A State-of-the-Art Review

2014 ◽  
Vol 919-921 ◽  
pp. 1755-1759
Author(s):  
Xue Yu Xiong ◽  
Sen Zhang ◽  
Li Jun Wang ◽  
Rong Jun Xue
Keyword(s):  
Experimental Data ◽  
Constitutive Relation ◽  
State Of The Art ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Future Research ◽  
State Of Art

An in depth state-of-art review is done on the topic,constitutive relations of masonry under compression. 12 constitutive models of masonry proposed by scholars from home and abroad are presented in the paper. These models can be classified into four types. Merits and drawbacks of each constitutive relation are discussed. Ten typical constitutive relations are selected to make comparisons. Results show that the ascending branch of curves has few differences, major differences occur in the descending branch of curves. Besides, two experimental data are used to analyze the models and results are discussed. Furthermore, some suggestions on this topic in future research are presented.

scholarly journals Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete

2018 ◽  
Vol 8 (9) ◽  
pp. 1609 ◽  
Author(s):  
Jinquan Zhang ◽  
Bing Han ◽  
Hui-Bing Xie ◽  
Li Zhu ◽  
Gang Zheng ◽  
...  
Keyword(s):  
Experimental Data ◽  
Sound Velocity ◽  
Axial Compression ◽  
Wave Velocity ◽  
Constitutive Relation ◽  
Constitutive Relations ◽  
Sound Signal ◽  
Coda Wave ◽  
Wave Interference ◽  
Loading And Unloading

Stresses in structures are usually converted by measured strains based on corresponding constitutive relations of materials. However, it is difficult to determine the constitutive relation of the material accurately, which leads to significant uncertainty of the converted stresses. This paper proposed a method to estimate the stresses in concrete by using the coda wave interference technique and established a model to describe the relation between the deformation of microcracks and the sound velocity. Based on the experiments, the development law of the coda waves with different frequencies of sound signal propagating in concrete was verified and discussed, and the change of the coda wave velocity during the loading and unloading of the specimen was tested. Parameters involved in the established model were regressed according to the experimental data. The analysis results show that the method can be used to test concrete stress and has a desirable accuracy.

Failure Prediction of Unidirectional Composites Undergoing Large Deformations1

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
Jacob Aboudi ◽  
Konstantin Y. Volokh
Keyword(s):  
Strain Energy ◽  
Large Deformations ◽  
Static Stability ◽  
Energy Functions ◽  
Micromechanical Analysis ◽  
Hyperelastic Materials ◽  
Failure Envelopes ◽  
Special Cases ◽  
Enhanced Strain ◽  
Strain Energy Functions

In previous publications, strain-energy functions with limiters have been introduced for the prediction of onset of failure in monolithic isotropic hyperelastic materials. In the present investigation, such enhanced strain-energy functions whose ability to accumulate energy is limited have been incorporated with a finite strain micromechanical analysis. As a result, macroscopic constitutive equations have been established which are capable to predict the onset of loss of static stability in a hyperelastic phase of composite materials undergoing large deformations. The details of the micromechanical analysis, based on a tangential formulation, for composites with periodic microstructure are presented. The derived micromechanical analysis includes the capability to model a possible imperfect bonding between the composite’s constituents and to provide the field distribution in the composite. The micromechanical method is verified by comparison with analytical and finite difference solutions for porous hyperelastic materials that are valid in some special cases. Results are given for a rubberlike matrix characterized by softening hyperelasticity, reinforced by unidirectional nylon fibers. The response of the composite to various types of loadings is presented up to the onset of loss of static stability at a location within the hyperelastic rubber constituent, and initial failure envelopes are shown.

Diagnostics of metal samples using the results of experimental and theoretical study of positively charged microparticles formed upon sample destruction

2018 ◽  
Vol 84 (10) ◽  
pp. 23-28
Author(s):  
D. A. Golentsov ◽  
A. G. Gulin ◽  
Vladimir A. Likhter ◽  
K. E. Ulybyshev
Keyword(s):  
Experimental Data ◽  
Early Stage ◽  
Experimental Studies ◽  
Material Model ◽  
Total Charge ◽  
Cross Sectional ◽  
Practical Applications ◽  
Mechanical And Electrical Properties ◽  
Order Of Magnitude ◽  
Using Data

Destruction of bodies is accompanied by formation of both large and microscopic fragments. Numerous experiments on the rupture of different samples show that those fragments carry a positive electric charge. his phenomenon is of interest from the viewpoint of its potential application to contactless diagnostics of the early stage of destruction of the elements in various technical devices. However, the lack of understanding the nature of this phenomenon restricts the possibility of its practical applications. Experimental studies were carried out using an apparatus that allowed direct measurements of the total charge of the microparticles formed upon sample rupture and determination of their size and quantity. The results of rupture tests of duralumin and electrical steel showed that the size of microparticles is several tens of microns, the particle charge per particle is on the order of 10–14 C, and their amount can be estimated as the ratio of the cross-sectional area of the sample at the point of discontinuity to the square of the microparticle size. A model of charge formation on the microparticles is developed proceeding from the experimental data and current concept of the electron gas in metals. The model makes it possible to determine the charge of the microparticle using data on the particle size and mechanical and electrical properties of the material. Model estimates of the total charge of particles show order-of-magnitude agreement with the experimental data.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

Stress Optical Behavior of Rubber Networks at Large Deformations

1966 ◽  
Vol 39 (5) ◽  
pp. 1436-1450
Author(s):  
K. J. Smith ◽  
D. Puett
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Statistical Theory ◽  
Natural Rubber ◽  
Large Deformations ◽  
Strong Support ◽  
Theoretical Development ◽  
Statistical Parameters ◽  
Strain Behavior ◽  
Optical Behavior

Abstract The birefringence of natural rubber networks at large deformations has been investigated experimentally and compared with the simultaneously determined stress—strain behavior. Our data is analyzed using a statistical theory of flexibly jointed chains, derived herein, which is believed to be more significant for the particular range of deformation used than the theories of Treloar and of Kuhn and Grün. In addition, the experimental data of Saunders is commented on in light of our theoretical development. We find that for network extensions exceeding those of the Gaussian region there is little correlation between the observed and theoretical behavior of the stress and birefringence (based upon the theory of flexibly jointed chains) and this lack of agreement is attributed to the fact that the statistical parameters needed for the description of the optical chain properties differ in magnitude from those required for the mechanical properties. Furthermore, by considering the points of incipient crystallization the strain behavior of the stress-optical coefficient is highly indicative of nonGaussian behavior rather than crystallization, and therefore yields strong support for the position that nonGaussian behavior does exist in rubber networks.

Investigation on hydrodynamic forces leading to coarse particle entrainment using Large-Eddy Simulations

2021 ◽  
Author(s):  
Gaston Latessa ◽  
Angela Busse ◽  
Manousos Valyrakis
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Large Scale ◽  
Large Eddy Simulations ◽  
Flow Conditions ◽  
Mean Flow ◽  
Protection Measures ◽  
Practical Applications ◽  
Particle Entrainment ◽  
Large Eddy

<p>The prediction of particle motion in a fluid flow environment presents several challenges from the quantification of the forces exerted by the fluid onto the solids -normally with fluctuating behaviour due to turbulence- and the definition of the potential particle entrainment from these actions. An accurate description of these phenomena has many practical applications in local scour definition and to the design of protection measures.</p><p>In the present work, the actions of different flow conditions on sediment particles is investigated with the aim to translate these effects into particle entrainment identification through analytical solid dynamic equations.</p><p>Large Eddy Simulations (LES) are an increasingly practical tool that provide an accurate representation of both the mean flow field and the large-scale turbulent fluctuations. For the present case, the forces exerted by the flow are integrated over the surface of a stationary particle in the streamwise (drag) and vertical (lift) directions, together with the torques around the particle’s centre of mass. These forces are validated against experimental data under the same bed and flow conditions.</p><p>The forces are then compared against threshold values, obtained through theoretical equations of simple motions such as rolling without sliding. Thus, the frequency of entrainment is related to the different flow conditions in good agreement with results from experimental sediment entrainment research.</p><p>A thorough monitoring of the velocity flow field on several locations is carried out to determine the relationships between velocity time series at several locations around the particle and the forces acting on its surface. These results a relevant to determine ideal locations for flow investigation both in numerical and physical experiments.</p><p>Through numerical experiments, a large number of flow conditions were simulated obtaining a full set of actions over a fixed particle sitting on a smooth bed. These actions were translated into potential particle entrainment events and validated against experimental data. Future work will present the coupling of these LES models with Discrete Element Method (DEM) models to verify the entrainment phenomena entirely from a numerical perspective.</p>

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

scholarly journals Optimal Strategy to Certify Quantum Nonlocality

2021 ◽  
Author(s):  
S. Gómez ◽  
D. Uzcátegui ◽  
I. Machuca ◽  
E. S. Gómez ◽  
S. P. Walborn ◽  
...  
Keyword(s):  
Experimental Data ◽  
Random Number ◽  
Bell Inequality ◽  
Random Number Generation ◽  
Quantum Nonlocality ◽  
Entangled Photons ◽  
Challenging Problem ◽  
Practical Applications ◽  
Variable Limit ◽  
The One

Abstract Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is only weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represent an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

scholarly journals Constitutive Relation for Large Deformations of Fiber-Reinforced Rubberlike Materials with Different Response in Tension and Compression

2016 ◽  
Vol 44 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Qian Li ◽  
David A. Dillard ◽  
Romesh C. Batra
Keyword(s):  
Constitutive Relation ◽  
Large Deformations ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Strain Tensor ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
Tension And Compression ◽  
Different Response ◽  
Rubberlike Materials

ABSTRACT Fiber-reinforced rubberlike materials commonly used in tires undergo large deformations and exhibit different responses in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function in terms of the five invariants of the right Cauchy-Green strain tensor and account for different response in tension and compression along the fiber direction. The constitutive relation accounts for both material and geometric nonlinearities and incorporates effects of the fifth strain invariant, I5. It has been shown by Merodio and Ogden that in shear dominated deformations, I5 makes a significant contribution to the stress-strain curve. We have implemented the proposed constitutive relation in the commercial software, LS-DYNA. The numerical solutions of a few boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which part of the solution is assumed and unknowns in the presumed solution are found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. When test data become available, one can modify the form of the strain energy density and replace the proposed constitutive relation by the new one in LS-DYNA.

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