On the Crucial Role of Imperfections in Quasi-static Viscoplastic Solutions

1991 ◽  
Vol 58 (3) ◽  
pp. 658-665 ◽  
Author(s):  
T. Belytschko ◽  
B. Moran ◽  
M. Kulkarni
Keyword(s):  
Shear Band ◽  
Strain Softening ◽  
Shear Bands ◽  
Step Function ◽  
Viscoplastic Material ◽  
One Dimensional ◽  
Initial Imperfections ◽  
Dimensional Boundary ◽  
The Stability

The stability and structure of shear bands and how they relate to initial imperfections is studied within the framework of a one-dimensional boundary value problem. It is shown that in strain-softening viscoplasticity the structure of the band depends on the structure of the imperfection. A Fourier analysis shows that the width of the shear band depends directly on the width of the imperfection, suggesting that the imperfection scales the response of the viscoplastic material. For continuously differentiable imperfections, the shear band is continuously differentiable, whereas when the imperfection is C° at the maximum, the shear band is C°, and cusp-shaped. For step function imperfections, the shear band is shown to be a step function, but it is shown that this solution is unstable.

Stability and Imperfections in Quasistatic Viscoplastic Solutions

1990 ◽  
Vol 43 (5S) ◽  
pp. S251-S255 ◽  
Author(s):  
T. Belytschko ◽  
B. Moran ◽  
M. Kulkarni
Keyword(s):  
Strain Field ◽  
Strain Softening ◽  
Fourier Spectrum ◽  
Shear Bands ◽  
Closed Form Solution ◽  
Step Function ◽  
Form Solution ◽  
Viscoplastic Material ◽  
Strain Fields ◽  
The Stability

The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C0 and C1 imperfections lead to C0 and C1 strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.

Strain localization due to structural softening during pressure sensitive rate independent yielding

2013 ◽  
Vol 184 (4-5) ◽  
pp. 357-371 ◽  
Author(s):  
Laetitia Le Pourhiet
Keyword(s):  
Shear Band ◽  
Strain Softening ◽  
Shear Bands ◽  
Limit Load ◽  
Friction Angle ◽  
Stress Axis ◽  
Flow Rule ◽  
Finite Limit ◽  
Confining Stress ◽  
Pressure Sensitive

Abstract After giving a complete analytical solution for the strain softening model associated to Mohr-Coulomb non associated elasto-plastic flow rule (MC-model), the paper demonstrates that this rheology possesses a finite limit load which allows solving for strength drop as a boundary value problem. The MC-model produces a non-dimensional strength drop, which depends on three parameters: the orientation of the shear band versus the least principal stress axis outside the band α0, the peak friction angle φ and the dilatation angle Ψ. The maximum reduction of strength obtained with that strain-softening model is on the order of the confining stress p0. For this weakest regime, the effective friction of the shear band drops from μini = 0.85 at peak to μss = 0.64 at the end of the softening phase. In this model, which considers thick shear bands, the weakest regime is not obtained for an orientation corresponding to the exact Coulomb orientation. Instead, the orientation of the weakest shear zone systematically deviates from the coulomb orientation by an angle, which rises with its internal friction angle. The characteristic shear strain needed to achieve steady state is quantified semi analytically and in the range of parameters valid for Earth, this strain is found to be of the order of 7–8%. These numbers are typical of what is observed in the laboratory, which give us confidence on that MC-model is a good and probably the simplest model to localize strain in numerical codes aimed at modeling the brittle part of the Earth.

scholarly journals A one-dimensional tearing mode equation for pedestal stability studies in tokamaks

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
J. W. Connor ◽  
R. J. Hastie ◽  
C. Marchetto ◽  
C. M. Roach
Keyword(s):  
Cross Section ◽  
Approximate Equation ◽  
Stability Studies ◽  
Dimensional Model ◽  
Tearing Mode ◽  
One Dimensional ◽  
Tearing Modes ◽  
The Stability ◽  
Poloidal Flux

Starting from expressions in Connor et al. (Phys. Fluids, vol. 31, 1988, p. 577), we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna & Callen (Phys. Plasmas, vol. 1, 1994, p. 2308) and Nishimura et al. (Phys. Plasmas, vol. 5, 1998, p. 4292), but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. the Joint European Torus (JET). We discuss how this one-dimensional model for tearing modes, which assumes a single poloidal harmonic for the perturbed poloidal flux, compares with a model that includes poloidal coupling Fitzpatrick et al. (Nucl. Fusion, vol. 33, 1993, p. 1533).

Shear band multiplication aided by free volume underthree-point bending

2010 ◽  
Vol 25 (2) ◽  
pp. 283-291 ◽  
Author(s):  
Lincai Zhang ◽  
Feng Jiang ◽  
Yanglei Zhao ◽  
Shibin Pan ◽  
Lin He ◽  
...  
Keyword(s):  
Shear Band ◽  
Free Volume ◽  
Shear Banding ◽  
Stress Gradient ◽  
Shear Bands ◽  
Bending Test ◽  
Three Point Bending ◽  
Deformation Ability ◽  
Plate Geometry

Zr52.5Cu17.9Ni14.6Al10Ti5 bulk metallic glass (BMG) alloy samples in both rod and plate geometry were prepared. Different free volume states were obtained through thermal treatment. The plastic deformation ability of the BMGs was investigated through both a three-point bending test and compression test. The three-point bending results reveal the important role of free volume content on the formation of multiple shear bands, as the shear band propagation can be efficiently stopped due to the existence of the stress gradient from the surface to the neutral plane. In compression, the sample size rather than free volume controls the shear banding behavior.

Role of free volume in strain softening of as-cast and annealed bulk metallic glass

2009 ◽  
Vol 24 (4) ◽  
pp. 1405-1416 ◽  
Author(s):  
Byung-Gil Yoo ◽  
Kyoung-Won Park ◽  
Jae-Chul Lee ◽  
U. Ramamurty ◽  
Jae-il Jang
Keyword(s):  
Shear Band ◽  
Metallic Glass ◽  
Bulk Metallic Glass ◽  
Free Volume ◽  
Structural Relaxation ◽  
Strain Softening ◽  
Plastic Zone Size ◽  
Number Density ◽  
Band Number

Plasticity in amorphous alloys is associated with strain softening, induced by the creation of additional free volume during deformation. In this paper, the role of free volume, which was a priori in the material, on work softening was investigated. For this, an as-cast Zr-based bulk metallic glass (BMG) was systematically annealed below its glass transition temperature, so as to reduce the free volume content. The bonded-interface indentation technique is used to generate extensively deformed and well defined plastic zones. Nanoindentation was utilized to estimate the hardness of the deformed as well as undeformed regions. The results show that the structural relaxation annealing enhances the hardness and that both the subsurface shear band number density and the plastic zone size decrease with annealing time. The serrations in the nanoindentation load-displacement curves become smoother with structural relaxation. Regardless of the annealing condition, the nanohardness of the deformed regions is ∼12–15% lower, implying that the prior free volume only changes the yield stress (or hardness) but not the relative flow stress (or the extent of strain softening). Statistical distributions of the nanohardness obtained from deformed and undeformed regions have no overlap, suggesting that shear band number density has no influence on the plastic characteristics of the deformed region.

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

The Role of Hydrophobicity in the Stability and pH-Switchability of (RXDX)4 and Coumarin-RXDX Conjugate β-Sheets

2020 ◽  
Author(s):  
Ryan Weber ◽  
Martin McCullagh
Keyword(s):  
Biological Imaging ◽  
Ph Sensing ◽  
Hydrophobic Residue ◽  
Ideal Candidate ◽  
Self Assembling ◽  
Sensing Applications ◽  
Β Sheets ◽  
The Stability ◽  
Dynamics Simulations

<p>pH-switchable, self-assembling materials are of interest in biological imaging and sensing applications. Here we propose that combining the pH-switchability of RXDX (X=Ala, Val, Leu, Ile, Phe) peptides and the optical properties of coumarin creates an ideal candidate for these materials. This suggestion is tested with a thorough set of all-atom molecular dynamics simulations. We first investigate the dependence of pH-switchabiliy on the identity of the hydrophobic residue, X, in the bare (RXDX)<sub>4</sub> systems. Increasing the hydrophobicity stabilizes the fiber which, in turn, reduces the pH-switchabilty of the system. This behavior is found to be somewhat transferable to systems in which a single hydrophobic residue is replaced with a coumarin containing amino acid. In this case, conjugates with X=Ala are found to be unstable and both pHs while conjugates with X=Val, Leu, Ile and Phe are found to form stable β-sheets at least at neutral pH. The (RFDF)<sub>4</sub>-coumarin conjugate is found to have the largest relative entropy value of 0.884 +/- 0.001 between neutral and acidic coumarin ordering distributions. Thus, we posit that coumarin-(RFDF)<sub>4</sub> containing peptide sequences are ideal candidates for pH-sensing bioelectronic materials.</p>

Metal-Metal Cooperative Bond Activation by Heterobimetallic Alkyl, Aryl, and Acetylide PtII/CuI Complexes

2020 ◽  
Author(s):  
Shubham Deolka ◽  
Orestes Rivada Wheelaghan ◽  
Sandra Aristizábal ◽  
Robert Fayzullin ◽  
Shrinwantu Pal ◽  
...  
Keyword(s):  
Alkyl Group ◽  
Bond Activation ◽  
Bond Cleavage ◽  
Terminal Alkyne ◽  
Alkyl Aryl ◽  
Metal Metal ◽  
The Stability ◽  
Selective Formation ◽  
Organoplatinum Compounds

We report selective formation of heterobimetallic PtII/CuI complexes that demonstrate how facile bond activation processes can be achieved by altering reactivity of common organoplatinum compounds through their interaction with another metal center. The interaction of the Cu center with Pt center and with a Pt-bound alkyl group increases the stability of PtMe2 towards undesired rollover cyclometalation. The presence of the CuI center also enables facile transmetalation from electron-deficient tetraarylborate [B(ArF)4]- anion and mild C-H bond cleavage of a terminal alkyne, which was not observed in the absence of an electrophilic Cu center. The DFT study indicates that the role of Cu center acts as a binding site for alkyne substrate, while activating its terminal C-H bond.

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