Analysis of Large Deformation Wound Roll Models

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
C. Mollamahmutoglu ◽  
J. K. Good
Keyword(s):  
Large Deformation ◽  
Deformation Theory ◽  
Computation Time ◽  
Small Deformation ◽  
Linear Analysis ◽  
Strain Theory ◽  
Metal Foil ◽  
Linear Strain ◽  
Almost All ◽  
Deformation Models

Almost all winding models incorporate the assumption of small linear deformations and strain in their development. These models treat the addition of a layer of web to a winding roll with linear analysis using linear strain theory. Very few winding models have been developed that incorporate large deformation theory although many models treat material nonlinearity. Tissue and nonwoven webs are highly extensible in-plane and highly compressible in the thickness dimension when compared to paper, plastic film, and metal foil webs. Winding models that embody large deformation theory should apply to all web materials. Such models may be wasteful in computation time for web materials such as paper, film, and foils where models that employ small deformation theory may provide sufficient accuracy. This would appear deterministic based upon the extensibility and compressibility of a web material, but the issue becomes more complex due to limitations in tension that can be exerted on the webs. Herein, a large deformation winding model will be developed. Results from this model will be used to benchmark results from other small and large deformation models, and with laboratory test data, a review of all results will be used to determine when or if large deformation winding models are required.

scholarly journals A new approach for the fracture grouting pressure in soil mass

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878643
Author(s):  
Zhi-bin Wang ◽  
Jin-feng Zou ◽  
Hai Yang
Keyword(s):  
Large Deformation ◽  
Failure Criterion ◽  
Deformation Theory ◽  
Small Deformation ◽  
Soil Mass ◽  
Parameter Analysis ◽  
Strength Failure ◽  
Grouting Pressure ◽  
Fracture Grouting ◽  
Coulomb Failure Criterion

This study focuses on analytical solutions of the fracture grouting pressure. Based on the cavity expansion and fracture grouting mechanism, the small deformation in the elastic zone, large deformation in the plastic zone, and non-associated flow rules are assumed. The solutions of the fracture grouting pressure based on the Unified Strength failure criterion, spatial mobilized plane criterion, Mohr–Coulomb failure criterion, and modified Cambridge model (MMC) are proposed for the large-deformation and small-deformation assumptions, respectively. A parameter analysis was conducted to analyze the differences between large-deformation and small-deformation theories. A comparison of the local test data with theoretical results reveals that the Cambridge model is more suitable for weakly consolidated soil and that the Mohr–Coulomb theory is suitable for over-consolidated soil. For all yield criteria in the study, the analysis indicates that the large-deformation theory has more reliable results than the small-deformation theory. The results in this study can direct the design and operation of fracture grouting.

Large-Deformation Theory of Shells of Revolution

1967 ◽  
Vol 34 (1) ◽  
pp. 56-58 ◽  
Author(s):  
W. Flu¨gge ◽  
S-C. Chou
Keyword(s):  
Internal Pressure ◽  
Large Deformation ◽  
Deformation Theory ◽  
Large Deflection ◽  
Small Strain ◽  
Strain Theory ◽  
Large Strains ◽  
Shells Of Revolution ◽  
Elastic Strains ◽  
Theory Of Shells

In this paper, nonlinear membrane equations are derived for a shell of revolution under the assumption that not only are the displacements and rotations large, but that, also, large strains are admitted. The equations, therefore, are aimed at shells which are not only very thin, but which are also made of a material which permits large elastic strains. The special difficulties resulting from this extension of the theory are discussed. As an example for the application of the equations, a circular toroid subjected to internal pressure is studied. Numerical results are given for a level of loading which lies clearly outside the domain of a large-deflection, small-strain theory.

scholarly journals Small and large deformation models of post-buckled beams under lateral constraints

2017 ◽  
Vol 24 (2) ◽  
pp. 386-405 ◽  
Author(s):  
Pengcheng Jiao ◽  
Amir H Alavi ◽  
Wassim Borchani ◽  
Nizar Lajnef
Keyword(s):  
Large Deformation ◽  
Computational Cost ◽  
Small Deformation ◽  
Theoretical Models ◽  
Deformation Model ◽  
Buckling Mode ◽  
Beam Shape ◽  
Post Buckling ◽  
The Difference ◽  
Deformation Models

This study aims at theoretically and experimentally investigating the buckling behavior of bilaterally constrained beams with respect to different geometric parameters and conditions. The theoretical models are developed based on small and large deformation theories, respectively. The nonlinear Euler–Bernoulli beam theory is used to form the governing equations. An energy method is introduced to solve the equilibrium beams by minimizing the total potential energy with respect to the weight coefficients of the buckling modes. The theoretical models are compared with experiments. Good agreements are obtained with respect to the force–displacement relationship and deformed beam shape configuration. This study indicates that the small deformation model is insufficient in predicting beam end shortening since the longitudinal displacement is negligible in the model. The large deformation model effectively predicts severe deflection of beams in terms of end shortening and rotation. Parametric studies are carried out to indicate the applicability of the presented models. In particular, the small deformation model is defined as “more applicable” when the difference of the post-buckling response between the small and large deformation models is less than 5% (Diff < 5%), given that its computational cost is generally smaller than the large model. In contrast, when the difference is greater than 5%, the large deformation model is suggested. In the end, a polynomial function is fitted to define the relationship between the ratio of net gap-to-beam length η and highest achievable buckling mode Φ. The presented small and large deformation models are effective in understanding and predicting the post-buckling responses of laterally confined beams under different conditions.

A Study of the Effect of Pre-Straining on Angular Distortion in One-Pass Fillet Welding Incorporating Large Deformation Theory

1995 ◽  
Vol 209 (5) ◽  
pp. 401-409 ◽  
Author(s):  
K-Y Bae ◽  
S-J Na
Keyword(s):  
Large Deformation ◽  
Initial Stress ◽  
Deformation Theory ◽  
Small Deformation ◽  
Angular Distortion ◽  
Stress Effect ◽  
The Finite Element Method ◽  
Concentrated Load ◽  
Fillet Welding ◽  
Updated Lagrangian

By using the finite element method based on the large deformation theory, the effect of pre-straining on angular distortion of one-pass fillet weldments was analysed for the free-end and constrained-end condition. Pre-straining by an additional concentrated load caused a large thermal deformation during heating, and reduced the reverse distortion during cooling and consequently the residual distortion. Geometric change of the fillet weldment caused by pre-straining during welding induced an initial stress effect on the stiffness to the further deformation, which is due to a developed in-plane stress. This initial stress effect could be considered in the large deformation theory to be based on the updated Lagrangian method, while it could not in the small deformation theory. As the pre-straining load increased in the free-end condition, the initial stress effect also increased. In the constrained-end condition, the initial stress effect played an important role in the deformation of the fillet weldment, even without pre-straining. By comparing the results predicted by the large deformation theory with those by the small deformation theory and experiments, it can be shown that the large deformation theory is able to describe the distortion phenomenon in fillet welding reasonably well.

Research on Creep Behavior of Three-Point Bending Specimen with Fixed Constraints at the Large Deformation Stage

2021 ◽  
Author(s):  
Xiao Han ◽  
Haiyang Yu ◽  
Guo-Yan Zhou ◽  
Fakun Zhuang ◽  
Shan-Tung Tu
Keyword(s):  
Aluminum Alloy ◽  
Large Deformation ◽  
Creep Deformation ◽  
Deformation Theory ◽  
Equivalent Stress ◽  
Small Deformation ◽  
Test Technique ◽  
Three Point Bending ◽  
Deformation Stage ◽  
General Deformation

Abstract Three-point bending specimen with fixed constraints (TPBSF) is a novel small specimen test technique, which can simultaneously obtain creep deformation and creep fracture data. However, the current researches are only focused on the small deformation theoretical analysis, which is contrary to the actual experiment results. In this study, the general deformation theory was introduced to analyze creep deformation behavior of TPBSF at the large deformation stage. Based on this theory, the equivalent stress and strain were analyzed. Then the feasibility and accuracy were verified by comparing with the experimental data of A7N01 aluminum alloy at 380 ?. The results show that the regressed creep parameters agree well with those from the uniaxial ones. It can be found that the equivalent stress obtained by the general deformation theory can be well used to life prediction analysis of A7N01 aluminum alloy.

scholarly journals Mechanics of moving defects in growing sheets: 3-d, small deformation theory

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Amit Acharya ◽  
Shankar C. Venkataramani
Keyword(s):  
Deformation Theory ◽  
Small Deformation

Mechanical properties of the tadpole tail fin

1998 ◽  
Vol 201 (19) ◽  
pp. 2691-2699 ◽  
Author(s):  
PA Doherty ◽  
RJ Wassersug ◽  
JM Lee
Keyword(s):  
Stress Relaxation ◽  
Large Deformation ◽  
Forced Vibration ◽  
Viscoelastic Properties ◽  
Developmental Plasticity ◽  
Rana Catesbeiana ◽  
Small Deformation ◽  
Collagen Fibres ◽  
Tadpole Tail ◽  
Undulatory Swimming

The tadpole tail fin is a simple double layer of skin overlying loose connective tissue. Collagen fibres in the fin are oriented at approximately +/-45 degrees from the long axis of the tail. Three tests were conducted on samples of the dorsal tail fin from 6-10 Rana catesbeiana tadpoles to establish the fin's viscoelastic properties under (1) large-deformation cyclic loading at 1 and 3 Hz, (2) small-deformation forced vibration at 1 and 3 Hz, and (3) stress relaxation under a 0.1 s loading time. The fin was very fragile, failing easily under tensile loads less than 7 g. It was also strikingly viscoelastic, as demonstrated by 72+/-1 % hysteresis loss (at 3 Hz), 16+/-3 % stress remaining after 100 s of stress relaxation and a phase angle of 18+/-1 degrees in forced vibration. As a consequence of its viscoelastic properties, the fin was three times stiffer in small than in large deformation. This may account for the ability of the fin to stay upright during normal undulatory swimming, despite the absence of any skeletal support. Tadpoles in nature are often found with damaged tails. We suggest that the unusually viscoelastic and fragile nature of the fin helps tadpoles escape the grasp of predators. Because the fin deforms viscoelastically and tears easily, tadpoles can escape predators and survive otherwise lethal attacks with only minor lacerations to the fin. Recent studies have shown that certain tadpoles develop taller fins in the presence of predators. This developmental plasticity is consistent with the tail fin acting as a protective but expendable 'wrap' around the core muscle tissue.

Test of Strain-Time Correspondence Principle with Gel-Containing Elastomers

1986 ◽  
Vol 59 (2) ◽  
pp. 305-314 ◽  
Author(s):  
N. Nakajima ◽  
E. R. Harrell
Keyword(s):  
Large Deformation ◽  
Correspondence Principle ◽  
Small Deformation ◽  
Complex Viscosity ◽  
Shear Stresses ◽  
Growth Data ◽  
Stress Growth ◽  
Linear Viscoelastic ◽  
The Difference ◽  
Linear Viscoelastic Theory

Abstract With four NBR samples and one EPR, oscillatory measurements and stress-growth measurements were performed, the former being at very small deformation and the latter leading to large deformation. The Rheometrics mechanical spectrometer was used with a cone-plate fixture. The temperature was 100°C. The stress-growth data of NBR's, converted to complex viscosity-frequency data through the application of stress-time correspondence principle, were in good agreement with those observed in the oscillatory measurement. Thus, the stress-growth data including the large deformation were “linearized” to form a master curve. With the EPR sample, such a linearization was not necessary. The stress-growth data were adequately treated with the linear viscoelastic theory up to shear stresses approaching the steady state. The difference in behavior between the NBR's and EPR is caused by differences in type and extent of long branching and gel present in the samples.

Description of Large Deformation Problem Using Means of Visual Strain

2013 ◽  
Vol 275-277 ◽  
pp. 16-22
Author(s):  
You Liang Xu
Keyword(s):  
Constitutive Equation ◽  
Large Deformation ◽  
Strain Tensor ◽  
Visual Image ◽  
Linear Strain ◽  
Deformation Problem ◽  
Practical Engineering ◽  
Large Deformation Problem ◽  
Strain Tensors ◽  
Linear Strain Tensor

The constitutive equation of large deformation problem is closely related to geometric description. Nowadays, linear strain tensor is no longer unsuitable to describe large deformation. However, the existing non-linear strain tensors have complicated forms as well as no apparent geometric or physical meaning. While, the increment method is used to solve, however, convergence and efficiency are low sometimes. Thus the idea of visual strain tensor is proposed, with distinct meaning and visual image. Beside, it is likely to be used in engineering measurement, and it can be connected with measured constitutive equation directly. Thus this research provides a new idea and method for solving large-deformation problems in practical engineering.

Simulation of piano strings and a soundboard by a large deformation theory

2006 ◽  
Vol 120 (5) ◽  
pp. 3363-3363
Author(s):  
Isoharu Nishiguchi ◽  
Masataka Sasaki ◽  
Aki Yamamoto
Keyword(s):  
Large Deformation ◽  
Deformation Theory
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