A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening

Summary It is well known that deformation and/or strain of geological materials localize when they come close to the failure state. In the present: study, we try to analyze the deformation problem using a constitutive relation with strain hardening and strain softening. The constitutive model of a soft rock and overconsolidated clay using an elasto-plastic constitutive theory with memory was originally developed by Adachi and Oka. This type of formulation is shown to be easily applied to analyze the material behavior of strain softening because there is a similarity to that in viscoplasticity. Using the proposed model, the loss of uniqueness of the solution to the initial value problem can be avoided and a special or complicated numerical technique, e.g., an arc length method, does not need to be used. When we use constitutive equations with strain softening in a finite element analysis, there is a problem of strong mesh size dependency of numerical results. To remedy the mesh size dependency, we generalize the Adachi-Oka model based on the concept of non-localization by Bazant. We apply the proposed constitutive model to the behavior of a sedimentary soft rock in the drained triaxial compression test. It is found that mesh size dependency becomes smaller using the non-localization of the constitutive model.

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Eine Finite-Element-Analyse der lokalisierten Verformung von weichem Gestein bei einem Stoffgesetz mit Entfestigung

Übersicht Bekanntlich findet bei geologischen Stoffen in der Nähe des Versagenszustandes eine Lokalisierung der Verformung statt. Die Analyse dieses Problems wird in diesem Beitrag auf der Grundlage eines Stoffansatzes mit Ver- und Entfestigung unternommen. Entwickelt wurde das zugrunde gelegte elastischplastische Stoffmodell mit Gedächtnis von Adachi und Oka für weiches Gestein und übermäßig verdichteten Ton. Wegen der Ähnlichkeit zur Viskoplastizität läßt sich diese Formulierung des Stoffgesetzes leicht auf die Analyse des Verhaltens von entfestigendem Material anwenden, da der Eindeutigkeitsverlust der Lösung des Anfangswertproblems vermieden wird und besondere Rechenverfahren wie etwa die Bogenlängenmethode nicht benötigt werden. Bei der Benutzung von Stoffgesetzen in einer Finite-Element-Rechnung hängen die Ergebnisse stark von der Netzeinteilung ab. Um dies abzustellen, wird das Modell von Adachi und Oka auf der Grundlage von Bazant's Konzept der Nichtlokalisierung verallgemeinert. Anwendungsbeispiel ist das Verhalten von weichem Gestein im drainierten Triaxial-Test. Es zeigt sich, daß mit dem Konzept der Nichtlokalisierung im Stoffmodell der Einfluß der Netzeinteilung geringer wird.

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Presented at the workshop on Numerical Methods for Localization and Bifurcation of Granular bodies, held at the Technical University of Gdask (Poland), September 25–30, 1989.     

Kinetic study on photochromism of WO3 aqueous sol and its enhancement accompanying spectral changes by the addition of TiO2 aqueous sol

Photochromism of a WO₃ aqueous sol has been investigated in a nitrogen atmosphere under controlled temperature. Effects of ageing of the WO₃ sols, concentrations of WO₃ sols or Cl⁻ ion and temperature on the coloring rate were examined. The coloring rate was the first-order with respect of the WO₃ concentration. The coloring process was accelerated by an addition of TiO₂ aqueous sols. Spectral changes were measured using the mixing sol with various molar ratios (γ) of WO₃ and TiO₂. The absorption spectra changed from those having the single peak at 775 nm to those with two peaks at 640 and 980 nm. Such spectral transformation was ascribed to the structural change of the WO₃ nanoclusters, depending on the γ value and the concentration of Cl⁻ ion.     

Looking-glass synergistic pharmacological chaperones: DGJ and L-DGJ from the enantiomers of tagatose

The enantiomers of tagatose are converted to L-DGJ [a noncompetitive inhibitor of human lysosome α-galactosidase A (α-Gal A), K(i) 38.5 μM] and DGJ [a competitive inhibitor of α-Gal A, K(i) 15.1 nM] in 66% yield. L-DGJ and DGJ provide the first examples of pharmacological chaperones that (a) are enantiomeric iminosugars and (b) have synergistic activity with implications for the treatment of lysosomal storage disorders and other protein deficiencies.     

Total synthesis of polygalolide A

The total synthesis of polygalolide A was accomplished through intramolecular C-glycosylation of glucal modified with siloxyfuran. The siloxyfuran group and siloxy substituent at the C-3 position played crucial roles in allowing direct access to the highly substituted oxabicyclo[3.2.1] core skeleton with correct quaternary stereogenic centers.     

A new ring expansion for a chiral hexahydroazulene skeleton possessing an angular methyl group

A new synthetic route for a pseudoguaiane ring system is described. The synthesis features an Ireland-Claisen rearrangement for constructing the trans-fused ring system, followed by a new ring expansion to yield a bicyclo[5.3.0]decane ring system possessing an angular methyl group.     

Development of Small Drop-Weight Testing Machine Based on Electromagnetic Induction

Experimental Mechanics - The impact strengths of solder joints between an electrical substrate and millimeter- or micrometer-sized electrical components such as resistors and capacitors must be...     

Asymptotic completeness for long-range many-particle systems with Stark effect. II

We prove the existence and the asymptotic completeness of the Dollard-type modified wave operators for many-particle Stark Hamiltonians with long-range potentials.     

Current spreading effects in 680-nm-band self-sustained pulsating AlGalnP visible laser diodes

We have developed 680-nm-band AlGalnP visible laser diodes having very lowintensity noise with stable self-sustained pulsation. The pulsation characteristics were affected by current spreading outside the ridge stripe. We obtained AlGalnP visible laser diodes with stable self-sustained pulsation by optimizing the ridge structure. The lasers achieved relative intensity noise (RIN) as low as-136 dB Hz^–1 in the temperature range 20–50°C at 3 mW.     

Direct mono-phosphorylation of 1,3-diols. A synthesis of FTY720-phosphate

A novel method for selective and direct phosphorylation of various 1,3-diols using silver(I) oxide, tetrabenzyl pyrophosphate (TBPP), and tetrahexylammonium iodide affording mono-phosphates was developed. We applied the present method to the synthesis of FTY720-phosphate.