Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
G. O. Antoine ◽  
R. C. Batra
Keyword(s):  
Constitutive Relation ◽  
Axial Strain ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Low Velocity Impact ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Cauchy Stress ◽  
Peak Strain ◽  
Material Parameters

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden’s expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

scholarly journals Flow Laws For Glacier Ice: Comparison Of Numerical Predictions And Field Measurements

1990 ◽  
Vol 36 (124) ◽  
pp. 324-339 ◽  
Author(s):  
C.J. Van Der Veen ◽  
I.M. Whillans
Keyword(s):  
Velocity Profile ◽  
Constitutive Relation ◽  
Constitutive Relations ◽  
Field Measurements ◽  
Primary Creep ◽  
Surface Strain ◽  
Force Balance ◽  
Strain Rates ◽  
Numerical Predictions ◽  
Flow Laws

AbstractIce flow along the 20 km long strain network up-stream of the Dye 3 bore hole in Greenland is studied in detail. By solving the force-balance equations and using selected flow laws, stresses and strain-rates are calculated throughout the section of the ice sheet. The validity of the results is evaluated by comparison with the velocity profile derived from bore-hole-tilting measurements, and with observed surface strain-rates. A number of constitutive relations are tried and most predict a velocity profile at the bore-hole site that is in good agreement with that observed, if appropriate enhancement factors are used. However, there are major discrepancies between modelled and measured surface strain-rates. Use of Nye’s generalization of Glen’s flow law, or an anisotropic constitutive relation, requires unrealistically large along-flow variations in the enhancement factor. Inclusion of normal stress effects can lead to much better agreement, but it is possible that other processes, such as dynamic recrystallization or primary creep, should be included in the constitutive relation of polar ice.

Torsion of a Viscoelastic Cylinder

2000 ◽  
Vol 67 (2) ◽  
pp. 424-427 ◽  
Author(s):  
R. C. Batra ◽  
J. H. Yu
Keyword(s):  
Stress Tensor ◽  
Constitutive Relation ◽  
Linear Relation ◽  
Constitutive Relations ◽  
Strain Tensor ◽  
Time History ◽  
Cauchy Stress ◽  
Kirchhoff Stress Tensor ◽  
History Of ◽  
Energy Dissipated

Finite torsional deformations of an incompressible viscoelastic circular cylinder are studied with its material modeled by two constitutive relations. One of these is a linear relation between the determinate part of the second Piola-Kirchhoff stress tensor and the time history of the Green-St. Venant strain tensor, and the other a linear relation between the deviatoric Cauchy stress tensor and the left Cauchy-Green tensor, its inverse, and the time history of the relative Green-St. Venant strain tensor. It is shown that the response predicted by the latter constitutive relation is in better agreement with the test data, and this constitutive relation is used to compute energy dissipated during torsional oscillations of the cylinder. [S0021-8936(00)00502-X]

An implicit constitutive relation for describing the small strain response of porous elastic solids whose material moduli are dependent on the density

2021 ◽  
pp. 108128652110214
Author(s):  
KR Rajagopal
Keyword(s):  
Constitutive Relation ◽  
Constitutive Relations ◽  
Deformation Gradient ◽  
Short Note ◽  
Small Strain ◽  
Cauchy Stress ◽  
Porous Metals ◽  
Elastic Solids ◽  
Elastic Bodies ◽  
Implicit Equations

In this short note, we develop a constitutive relation that is linear in both the Cauchy stress and the linearized strain, by linearizing implicit constitutive relations between the stress and the deformation gradient that have been put into place to describe the response of elastic bodies (Rajagopal, KR. On implicit constitutive theories. Applications of Mathematics 2003; 28: 279–319), by assuming that the displacement gradient is small. These implicit equations include the classical linearized elastic constitutive approximation as well as some classes of constitutive relations that imply limiting strain in tension, as special subclasses. Moreover, the constitutive relations that are developed allow the material moduli to depend on the density; thus, they can be used to describe the response of porous materials, such as porous metals, bone, rocks, and concrete undergoing small deformations.

scholarly journals Experimental Study on Biaxial Dynamic Compressive Properties of ECC

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1257
Author(s):  
Shuling Gao ◽  
Guanhua Hu
Keyword(s):  
Strain Rate ◽  
Lateral Pressure ◽  
Deformation Modulus ◽  
Strain Curve ◽  
Peak Stress ◽  
Pressure Level ◽  
Strain Rates ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Toughness Index

An improved hydraulic servo structure testing machine has been used to conduct biaxial dynamic compression tests on eight types of engineered cementitious composites (ECC) with lateral pressure levels of 0, 0.125, 0.25, 0.5, 0.7, 0.8, 0.9, 1.0 (the ratio of the compressive strength applied laterally to the static compressive strength of the specimen), and three strain rates of 10−4, 10−3 and 10−2 s−1. The failure mode, peak stress, peak strain, deformation modulus, stress-strain curve, and compressive toughness index of ECC under biaxial dynamic compressive stress state are obtained. The test results show that the lateral pressure affects the direction of ECC cracking, while the strain rate has little effect on the failure morphology of ECC. The growth of lateral pressure level and strain rate upgrades the limit failure strength and peak strain of ECC, and the small improvement is achieved in elastic modulus. A two-stage ECC biaxial failure strength standard was established, and the influence of the lateral pressure level and peak strain was quantitatively evaluated through the fitting curve of the peak stress, peak strain, and deformation modulus of ECC under various strain rates and lateral pressure levels. ECC’s compressive stress-strain curve can be divided into four stages, and a normalized biaxial dynamic ECC constitutive relationship is established. The toughness index of ECC can be increased with the increase of lateral pressure level, while the increase of strain rate can reduce the toughness index of ECC. Under the effect of biaxial dynamic load, the ultimate strength of ECC is increased higher than that of plain concrete.

Strain Rate Evaluation of Some Typical Nuclear Power Plant Components During Plant Operation

2010 ◽  
Author(s):  
Koji Dozaki ◽  
Hiromasa Chitose ◽  
Hiroshi Ogawa ◽  
Hideo Machida
Keyword(s):  
Fatigue Life ◽  
Strain Rate ◽  
Strain History ◽  
Strain Rates ◽  
Peak Strain ◽  
Plant Operation ◽  
Thermal Transients ◽  
Reactor Water ◽  
Rate Evaluation ◽  
Reactor Internals

The dynamic aspects of loading conditions for reactor internals, piping and the like, are thought to play important roles in the initiation of failures due, for example, to stress corrosion cracking (SCC) and fatigue. Some reports show that a strain rate on the order of 10−7 s−1 most affects susceptibility to SCC in the BWR reactor water environment. Environmental fatigue, which exhibits a shorter fatigue life in reactor water than that in air, is considered to have a remarkable correlation with strain rate and its affect on fatigue life. Despite its significant affect on SCC and fatigue, the actual strain rate of components is not known and practical evaluation methods have not been developed; consequently, such failure modes as SCC and fatigue are not evaluated in design. For this paper, strain rates induced by dynamic loading during such operations as plant start-up were calculated at typical points, such as reactor internals, piping and so on. The finite element method was applied to calculate the strain history of each point, and the strain rate was evaluated. The strain rate evaluation results clearly demonstrated that thermal transients provide greater peak strain rate values than pressure transients. Strain rates on the order of 10−7 s−1 were obtained for most points of major components during such thermal transients as plant start-ups. The major factors determining the strain rate magnitude were discussed, based on the calculation results. It was shown that the rate of temperature rise was the most important parameter, because it exhibited much larger sensitivity than the other parameters on the strain rate and could be controlled by plant operation procedures. In addition, a simple strain rate evaluation method based on Green’s function was developed for a specific point with a given design condition.

Characteristics of Dynamic Recrystallization during Hot Deformation for High Nitrogen Stainless Steels

2012 ◽  
Vol 715-716 ◽  
pp. 115-121
Author(s):  
Hai Wen Luo ◽  
Xu Dong Fang ◽  
Rui Zhen Wang ◽  
Zhan Yin Diao
Keyword(s):  
Dynamic Recrystallization ◽  
Stainless Steels ◽  
Hot Deformation ◽  
Strain Rates ◽  
Peak Strain ◽  
High Nitrogen ◽  
Flow Curves ◽  
Grain Sizes ◽  
Nitrogen Contents ◽  
High Nitrogen Stainless Steel

Dynamic recrystallization was studied for the stainless steels with nitrogen contents of 0.56% to 1.08% during hot deformation at temperatures of 900~1200 with strain rates ranging from 0.003 to 42 s-1. It was found that flow stress could increase remarkably with increasing nitrogen content. Flow curves during the deformation by 0.1~42/s at temperatures of 900~1200°C show a single peak, indicating the occurrence of dynamic recrystallization during deformation. The peak strain seems to decrease with increasing N content, suggesting that higher content of N facilitates dynamic recrystallization. The quenched microstructures were analyzed by optical microscopy, EBSD and TEM. The recrystallized grain sizes on the quenched specimens were measured and its dependence on temperature and strain rate was analyzed. At high temperature, continuously dynamically recrystallized microstructures were observed; whilst at low temperature, necklace-like partially recrystallized microstructures were found. Key words: High nitrogen stainless steel; dynamic recrystallization; stress-strain curves

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

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