Atsushi Yashima

A strain localization analysis using a viscoplastic softening model for clay

Strain localization has become an attractive subject in geomechanics during the past decade. Shear bands are well known to develop in clay specimens during the straining process. Strain localization is closely related to plastic instability. In the present paper, a non-linear instability condition for the viscoplastic strain softening model during the creep process is firstly obtained. It is found that the proposed viscoplastic model is capable of describing plastic instability. Secondly, a two-dimensional linear instability analysis is performed and the preferred orientation for the growth of fluctuation and the instability condition are derived. It is worth noting that the two instability conditions are equivalent. Finally, the behavior of the clay is numerically analyzed in undrained plane-strain compression tests by the finite element method, considering a transport of pore water in the material at a quasi-static strain rate. The numerical results show that the model can predict strain localization phenomena, such as shear banding. From the numerical calculations, the effects of strain rate and permeability are discussed.

Instability of an elasto-viscoplastic constitutive model for clay and strain localization

Abstract A viscoplastic strain softening model is derived and the instability of the model during the creep process is discussed. It is found that the proposed viscoplastic model is capable of describing plastic instability. The applicability of the model is evaluated with the results of experiments on Osaka alluvial clay. Finally, we numerically analyze the behavior of the clay in undrained plane strain compression tests by the finite element method, considering a transport of pore water in the material at a quasi-static strain rate. The numerical results show that the model can predict strain localization phenomena, such as shear banding.

Instability of Gradient Dependent Viscoplastic Model for Clay Saturated With Water and FEM Analysis

For the last two decade, several constitutive models have been proposed for geomaterials and applied to practical problems. There remains, however, still some outstanding issues to be resolved. One of them is the formation of shear band before and after failure. This problem is strongly connected to the strain localization phenomenon. Recently, the importance of simulation of post localization regime has been pointed out. For this problem an interesting approach has been proposed by Aifantis and co-workers based on the introduction of higher order strain gradients into constitutive equation. The purpose of this paper is to propose a strain gradient dependent elastoviscoplastic model for clay and study the instability condition of the constitutive theory. The model is then implemented into FEM code to simulate the clay behavior under plane strain condition by considering the transport of pore water based on Biot`s theory of solid-fluid mixture. 22 refs., 7 figs.

The effect of stress induced anisotropy on shear band formation

SummaryThis paper describes the effect of non-coaxiality arising from material anisotropy on bifurcation phenomena such as shear band formation. The elasto-plastic model originally proposed by Sekiguchi and Ohta [7] is one of the typical models which include anisotropy and it is used to examine the effect of anisotropy on shear band formation. First, we shall extend this elasto-plastic model for infinitesimal strain to a model for finite strain and discuss the mathematical structure of this model. The stress induced anisotropy is found to bring about a vertex-like effect, such as the non-coaxiality between the Cauchy stress tensor and a plastic stretching tensor, into the constitutive relation. Then, we shall examine the effect of this non-coaxiality on bifurcation conditions in relation to the material rigidity which changes with the angle of simple shear. Finally, it will be concluded that this non-coaxiality arising from the anisotropy does not contribute much to triggering instability by localization of the deformations which result in shear band formation, while on the other hand, the non-coaxiality due to the yield vertex effect is rather inclined towards instability by localization of the deformations.ÜbersichtBeschrieben wird der Einfluß anisotropie-bedingt verschiedener Achsen von Spannung und Deformationsgeschwindigkeit auf Verzweigungsphänomene wie die Scherzonenbildung. Das elastisch-plastische Modell von Sekiguchi und Ohta wird als typisch anisotropes Modell zur Untersuchung des Einflusses der Anisotropie auf die Scherzonenbildung benutzt. Zunächst wird es zu einem Modell für endliche Deformationen erweitert und seine mathematische Struktur erörtert. Es zeigt sich, daß die spannungsinduzierte Anisotropie einen Effekt ähnlich einer Fließortspitze erzeugt wie z. B. verschiedene Achsen von Cauchy-Spannungstensor und plastischem Strecktensor. Danach wird in Zusammenhang mit der Materialsteifigkeit, die vom Winkel der einfachen Scherung abhängt, der Einfluß verschiedener Achsen auf Verzweigungsbedingungen untersucht. Es wird gefolgert, daß anisotropie-bedingt verschiedene Achsen wenig zur Auslösung der Instabilität durch lokalisierte Deformation beitragen, andererseits verschiedene Achsen infolge einer Fließortspitze die Neigung zur lokalisierten Deformation unterstützen.

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

SummaryIt 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.ÜbersichtBekanntlich 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 Bazants 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.

GRADIENT DEPENDENT VISCOPLASTIC MODEL FOR CLAY AND NUMERICAL EXPERIMENTS BY FEM

ABSTRACT A gradient dependent viscoplastic constitutive model for water saturated clay is proposed. A linear perturbation stability analysis is applied to this model. We disccussed the instability of this model and the application to a boundary value problem. Finally, we carried out a numerical experiment by using a finite element method.