Softening Instability: Part I—Localization Into a Planar Band

1988 ◽  
Vol 55 (3) ◽  
pp. 517-522 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Strain Softening ◽  
Geometrical Nonlinearity ◽  
Small Strain ◽  
Minimum Thickness ◽  
Infinite Layer ◽  
The Stability ◽  
Conditions Of Stability ◽  
Range Part ◽  
Homogeneous Strain ◽  
The Continuum

Distributed damage such as cracking in heterogeneous brittle materials may be approximately described by a strain-softening continuum. To make analytical solutions feasible, the continuum is assumed to be local but localization of softening strain into a region of vanishing volume is precluded by requiring that the softening region, assumed to be in a state of homogeneous strain, must have a certain minimum thickness which is a material property. Exact conditions of stability of an initially uniform strain field against strain localization are obtained for the case of an infinite layer in which the strain localizes into an infinite planar band. First, the problem is solved for small strain. Then a linearized incremental solution is obtained taking into account geometrical nonlinearity of strain. The stability condition is shown to depend on the ratio of the layer thickness to the softening band thickness. It is found that if this ratio is not too large compared to 1, the state of homogeneous strain may be stable well into the softening range. Part II of this study applies Eshelby’s theorem to determine the conditions of localization into ellipsoidal regions in infinite space, and also solves localization into circular or spherical regions in finite bodies.

Equilibrium Path Bifurcation Due to Strain-Softening Localization in Ellipsoidal Region

1990 ◽  
Vol 57 (4) ◽  
pp. 810-814 ◽  
Author(s):  
Z. P. Bazˇant
Keyword(s):  
Strain State ◽  
Strain Softening ◽  
Strain Diagram ◽  
Equilibrium Path ◽  
Loss Of Stability ◽  
Infinite Layer ◽  
Neutral Equilibrium ◽  
Homogeneous Strain ◽  
Preceding Study ◽  
Path Bifurcation

A preceding study of the loss of stability of a homogeneous strain state in infinite homogeneous solid due to localization of strain into an ellipsoidal region is complemented by determining the condition of bifurcation of equilibrium path due to ellipsoidal localization mode. The bifurcation occurs when the tangential moduli matrix becomes singular, which coincides with Hill’s classical bifurcation condition for localization into an infinite layer. The bifurcation is normally of Shanley type, occurring in absence of neutral equilibrium while the controlled displacements at infinity increase. During the loading process with displacement increase controlled at infinity, this type of bifurcation precedes the loss of stability of equilibrium due to an ellipsoidal localization mode, except when the tangential moduli change suddenly (which happens, e.g., when the slope of the stress-strain diagram is discontinuous, or when temperature is increased).

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals A Complete CDW Theory for the Single Ionization of Multielectronic Atoms by Bare Ion Impact

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 3
Author(s):  
Juan M. Monti ◽  
Michele A. Quinto ◽  
Roberto D. Rivarola
Keyword(s):  
Transition Amplitude ◽  
Emission Spectra ◽  
Heavy Ion ◽  
Distorted Wave ◽  
Single Ionization ◽  
Complete Form ◽  
Active Electron ◽  
Ion Impact ◽  
Range Part ◽  
The Continuum

A complete form of the post version of the continuum distorted wave (CDW) theory is used to investigate the single ionization of multielectronic atoms by fast bare heavy ion beams. The influence of the non-ionized electrons on the dynamic evolution is included through a residual target potential considered as a non-Coulomb central potential through a GSZ parametric one. Divergences found in the transition amplitude containing the short-range part of the target potential are avoided by considering, in that term exclusively, an eikonal phase instead of the continuum factor as the initial channel distortion function. In this way, we achieve the inclusion of the interaction between the target active electron and the residual target, giving place to a more complete theory. The present analysis is supported by comparisons with existing experimental electron emission spectra and other distorted wave theories.

Stability and collapse of holes in liquid layers

2018 ◽  
Vol 855 ◽  
pp. 1130-1155 ◽  
Author(s):  
Cunjing Lv ◽  
Michael Eigenbrod ◽  
Steffen Hardt
Keyword(s):  
Liquid Film ◽  
Power Laws ◽  
Theoretical Models ◽  
Liquid Volume ◽  
Capillary Length ◽  
Minimum Thickness ◽  
The Stability ◽  
Film Profile ◽  
Hole Closure ◽  
Good Agreement

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that$d_{c}$increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

scholarly journals Устойчивость углеродной нанолуковицы в контакте с графитовой подложкой

2019 ◽  
Vol 45 (12) ◽  
pp. 9
Author(s):  
С.Ш. Рехвиашвили ◽  
М.М. Бухурова
Keyword(s):  
Theoretical Model ◽  
Interaction Potential ◽  
Interatomic Interaction ◽  
Continuum Approximation ◽  
Graphite Phase ◽  
Interatomic Interaction Potential ◽  
The Stability ◽  
The Continuum

AbstractA theoretical model describing the stability of a carbon nano-onion in the presence of a bulk catalytic graphite phase is constructed based on the continuum approximation of interatomic interaction potential and mechanics of deformed systems. It is shown that a carbon nano-onion becomes unstable when its radius exceeds double value of the radius of a fullerene C_60 molecule.

A Comprehensive Energy Formulation for General Nonlinear Material Continua

1997 ◽  
Vol 64 (2) ◽  
pp. 353-360 ◽  
Author(s):  
A. Carini ◽  
O. De Donato
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Strain ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Total Potential ◽  
Initial Boundary Value ◽  
Energy Formulation ◽  
The Continuum

By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.

scholarly journals Factor of Safety Reduction Factors for Accounting for Progressive Failure for Earthen Levees with Underlying Thin Layers of Sensitive Soils

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Adam J. Lobbestael ◽  
Adda Athanasopoulos-Zekkos ◽  
Josh Colley
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Progressive Failure ◽  
Limit Equilibrium ◽  
Thin Layers ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Limit Equilibrium Methods ◽  
The Stability ◽  
Reduction Factors

The effects of progressive failure on flood embankments with underlying thin layers of soft, sensitive soils are investigated. Finite element analysis allows for investigation of strain-softening effects and progressive failure in soft and sensitive soils. However, limit equilibrium methods for slope stability analysis, widely used in industry, cannot capture these effects and may result in unconservative factors of safety. A parametric analysis was conducted to investigate the effect of thin layers of soft sensitive soils on the stability of flood embankments. A flood embankment was modeled using both the limit equilibrium method and the finite element method. The foundation profile was altered to determine the extent to which varying soft and sensitive soils affected the stability of the embankment, with respect to progressive failure. The results from the two methods were compared to determine reduction factors that can be applied towards factors of safety computed using limit equilibrium methods, in order to capture progressive failure.

scholarly journals The X-Ray Nova GRO J0422+32 in Decline and Quiescence

1996 ◽  
Vol 158 ◽  
pp. 399-400
Author(s):  
M. R. Garcia ◽  
P. J. Callanan ◽  
J. E. McClintock ◽  
P. Zhao
Keyword(s):  
Emission Line ◽  
Emission Region ◽  
Dwarf Novae ◽  
X Ray ◽  
First Order ◽  
Band Emission ◽  
Line Region ◽  
Hα Emission ◽  
The Stability ◽  
The Continuum

We have followed the X-ray nova GRO J0422+32, spectroscopically and photometrically, throughout the decline to quiescence.In the final stages of decay (days 430…880 after the outburst, see Callanan et al. (1995) for the epoch 1995), the equivalent width (EW) of the Hα emission increases monotonically and the R magnitude decreases monotonically. This suggests that the flux in the Hα line is constant, while the continuum fades. The Hα flux is the product of the R band flux (F(R), arbitrarily scaled to 100 at R = 19 mag) and the EW, and is shown in the last column of the table below. The Hα flux varies by only ~ 30% while the continuum fades by a factor of eight (from R = 19 mag to R = 21.3 mag). So, to first order, the Hα luminosity is constant in the final stages of decay. While it is generally the case that the emission line EWs in individual dwarf novae also increase during the decay, the exact behavior seen in GRO J0422+32 is not what is seen for dwarf novae (on average). Using the relation between EW[Hβ] and Mv given in figure 6 of Patterson (1984), we would expect a factor of ~ 5 variation in the Hα flux during days 430…880. The stability of the Hα flux implies that somehow the emission line region is ‘disconnected’ from the continuum (R–band) emission region.

Measurement of free-circulating cis-dichlorodiammineplatinum(II) in plasma.

1977 ◽  
Vol 23 (12) ◽  
pp. 2258-2262 ◽  
Author(s):  
S J Bannister ◽  
L A Sternson ◽  
A J Repta ◽  
G W James
Keyword(s):  
Exchange Resin ◽  
Cation Exchange Resin ◽  
Free Drug ◽  
Platinum Compounds ◽  
Minimum Thickness ◽  
X Ray ◽  
Drug Plasma ◽  
Detection Capabilities ◽  
The Stability ◽  
Bound Drug

Abstract Dichlorodiammineplatinum(II) is an anti-neoplastic agent that is currently undergoing clinical evaluation. We describe an analytical method for monitoring the free drug (or its breakdown products) in plasma. The method is able to distinguish between free and protein-bound drug. Plasma samples are deproteinized by centrifugal ultrafiltration. The platinum in the ultrafiltrate is converted to a cationic species by reaction with ethylenediamine and then collected on paper impregnated with cation-exchange resin. This process concentrates the samples, increases the stability of the platinum compounds (by removing the compound from solution), and places the sample in a uniform matrix of minimum thickness, which maximizes detection capabilities. Platinum was measured directly on the ion-exchange disks by X-ray fluorescence. The detection limit for free drug is 240 microgram/liter of plasma at the 3s level and fluorescence intensity is linearly related to drug concentration in the range from 570 to 5700 microgram/liter.

Stability Analysis of Plate-Cone Reticulated Shell

2011 ◽  
Vol 71-78 ◽  
pp. 3760-3763
Author(s):  
Xing Wang
Keyword(s):  
Stability Analysis ◽  
Bearing Capacity ◽  
Double Layer ◽  
Geometrical Nonlinearity ◽  
Ultimate Bearing Capacity ◽  
Arc Length ◽  
Stability Behavior ◽  
Destruction Mechanism ◽  
The Stability ◽  
Complete Process

This paper carries out stability analysis on plate-cone reticulated shell considering geometrical nonlinearity of cooperating work between plates and members. In this paper, stability behavior of different kinds of plate-cone reticulated shell considering geometrical nonlinearity is analyzed by using the software ANSYS, tracking complete process balance path for load-displacement by using arc-length method, the several problems of plate-cone reticulated shell are studied, such as destruction mechanism, structural ductility, ultimate bearing capacity and strength reserve, some important conclusions are obtained. After analyzing the stability behavior of double-layer reticulated shell by ANSYS and comparing with plate-cone reticulated shell, it is proved that plate-cone reticulated shell is more advantageous than double-layer reticulated shell in the aspect of stability behavior.

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