Relationships between Stress and Strain

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Free Energy ◽  
Closed System ◽  
Uniaxial Stress ◽  
Deformation Tensor ◽  
Stress And Strain ◽  
Stress Strain ◽  
Swelling Equilibrium ◽  
Simple Tension ◽  
Closed Systems ◽  
Link Model

In the first section of this chapter, the relationships between the Helmholtz free energy, the stress tensor, and the deformation tensor are given for uniaxial stress. These relations follow from the general discussion of stress and strain given in appendix C, and the notation and approach closely follow the classic treatment of Flory. The detailed forms of the stress-strain relations in simple tension (or compression) are given in the remaining sections of the chapter for the (1) phantom network, (2) affine network, (3) constrained-junction model, and (4) slip-link model. Results of theory are then compared with experiment. The effects of swelling on the stress-strain relations are also included in the discussion. It is to be noted that the stress-strain relations in this chapter are obtained by treating the swollen networks as closed systems. The conditions for such systems are fulfilled if solvent does not move in and out of the network during deformation. A network swollen with a nonvolatile solvent and subject to simple tension in air is an example of a closed system. The same network at swelling equilibrium and subjected to compression will exude some of the solvent under increased internal pressure, and is therefore not a closed system. For semiopen systems, such as those under compression, or, in general, networks stressed while immersed in solvent, a more general thermodynamic treatment is required. This situation will be taken up in the following chapter.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Calculations for Uniaxial Stress and Strain Cycling in Plasticity

1984 ◽  
Vol 51 (3) ◽  
pp. 487-493 ◽  
Author(s):  
P. M. Naghdi ◽  
D. J. Nikkel
Keyword(s):  
Type Theory ◽  
Uniaxial Stress ◽  
Mean Value ◽  
Stress And Strain ◽  
Material Response ◽  
Tension And Compression ◽  
Stress Cycling ◽  
The Mean ◽  
Rate Type ◽  
Strain Cycling

Within the framework of an existing purely mechanical, rate-type theory of plasticity, detailed calculations are presented for certain types of material response during stress and strain cycling in a uniaxial homogeneous deformation. These features pertain specifically to material response in stress cycling between fixed values of stress in tension and compression (not necessarily equal in magnitude) resulting in ratcheting of strain, and a type of saturation hardening caused by strain cycling between any two fixed values of strain when the mean value of stress (in tension and compression) tends to zero.

scholarly journals Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Longling Fan ◽  
Jing Yao ◽  
Chun Yang ◽  
Dalin Tang ◽  
Di Xu
Keyword(s):  
Wall Thickness ◽  
Material Properties ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain ◽  
Material Stiffness ◽  
The Mean ◽  
Lv Volume ◽  
Parameter Values

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress–strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress–strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole–diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Three Types of Stress-Strain Relationship’s Comparison of Circular Tubed Reinforced Concrete in FEA

2012 ◽  
Vol 204-208 ◽  
pp. 930-933
Author(s):  
Xiao Hu ◽  
Zhen Lin Chen
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Uniaxial Stress ◽  
Steel Tube ◽  
Finite Element Analyses ◽  
Stress Strain ◽  
Concrete Filled Steel Tube ◽  
Bearing Analysis

The paper introduces 3 types of uniaxial stress-strain relationships of concrete filled steel tube by Pan Youguang, Susantha and Saenz, and performs finite element analyses of the axial strengths of 18 CTRC columns, studies the characters of three models, and comprises between the axial strengths from FEA and existed experiments. Results show these 3 types of model are all suitable for bearing analysis, but Pan’s model is more accurate.

scholarly journals Theoretical and experimental method for determining elastic characteristics of nanomaterials

2019 ◽  
Vol 489 (5) ◽  
pp. 469-472
Author(s):  
V. M. Fomin ◽  
A. A. Filippov
Keyword(s):  
Mechanical Characteristics ◽  
Heterogeneous Material ◽  
Uniaxial Stress ◽  
Analytical Form ◽  
Mechanical Tests ◽  
Stress And Strain ◽  
Binder Phase ◽  
Homogeneous Materials ◽  
Silica Dioxide ◽  
Elastic Characteristics

The method allows determining the mechanical characteristic of nanoobjects was presented. A heterogeneous material consisting of a nanophase and a binder phase was considered, the mass and volume concentrations of components were given. Heterogeneous material is reduced to homogeneous by averaging methods while the mechanical characteristics will be associated with averaged ones. Assuming that the mechanical characteristics of the binder and averaged homogeneous materials are known from mechanical tests, the system of equations allow us to determine the mechanical characteristics of nanoobjects included in this heterogeneous material. It is believed that the mechanical characteristics of bonding and averaged homogeneous materials make it possible to obtain equations of equations that allow one to determine the mechanical characteristics of nano-objects present in this heterogeneous material. Classical mechanical tests were carried out, describing the uniaxial stress and strain states of materials, which made it possible to obtain an analytical form the dependences of the mechanical characteristics of nanophases depending on their size. Specific examples are given for silica dioxide nanoparticles (Aerosil and Tarkosil powders).

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