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| 1.
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Yatomi, Chikayoshi ; Nishihara, Akira ; 矢富, 盟祥 ; 西原, 晃
概要:
金沢大学理工研究域環境デザイン学系<br />Much attention has been paid to anisotropic behavior of soils, such as the inherent anisotropy an
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d the stress induced anisotropy. Nevertheless, they often appear in the literature without any clear definitions. In the theory of finite deformations, the concept of isotropy is well established and is clearly distinguishable from the objectivity. However, in the infinitesimal theory, which is usually assumed in soil mechanics, they seem to be in confusion and, as a result, even simple anisotropy is not clearly defined. In this paper, we therefore first discuss the general principles of constitutive equations in finite theories and in infinitesimal theories to make a clear distinction between the objectivity and the isotropy. One of our most important results is that, if reference vectors or tensors are employed, in infinitesimal theories, the objectivity requires that anisotropic materials can be represented by isotropic functions. Using a reference tensor, we finally give a clear definition of the inherent anisotropy and the stress induced anisotropy. We then examine their difinitions employing a concrete example and show how the principles derived are useful, including the failure condition and the materials of differential type.
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| 2.
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Yatomi, Chikayoshi ; Yashima, Atsushi ; Iizuka, Atsushi ; Sano, Ikuo ; 矢富, 盟祥 ; 八嶋, 厚 ; 飯塚, 敦 ; 佐野, 郁雄
概要:
金沢大学理工研究域環境デザイン学系<br />In order to simulate the formation of localized shear bands, which is commonly observed during la
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rge deformation of soils, we first present a systematic extension of the well known Cam-clay model developed for small strains to the model for finite strains/deformations and then incorporates a non-coaxial term in the model. Finally, confining the deformation to undrained plane strain conditions, we examine the effects of the non-coaxial term on the shear bands formation.
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| 3.
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Yatomi, Chikayoshi ; Yashima, Atsushi ; Iizuka, Atsushi ; Sano, Ikuo ; 矢富, 盟祥 ; 八嶋, 厚 ; 飯塚, 敦 ; 佐野, 郁雄
概要:
金沢大学理工研究域環境デザイン学系<br />This paper is concerned with the formation of the shear bands by employing the finite element met
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hod with a non-coaxial Cam-clay model developed in our last paper (Yatomi et al., 1989). This finite element method for finite strains is formulated as a soil/water coupling form based on the updated Lagrangean scheme. A demonstration of shear bands formation is given in a classical rigid punch problem without introducing any initial imperfections into the material elements.
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| 4.
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新保, 泰輝 ; 矢富, 盟祥 ; Shimbo, Taiki ; Yatomi, Chikayoshi
概要:
金沢大学理工研究域環境デザイン学系<br />In this paper, we present a new interpolation method expressing an arbitrary discontinuous curve
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with a high accuracy based on the B-Spline interpolation. We call it “The Heaviside B-Spline interpolation method”. The idea of this method is to use the Heaviside step function to construct a high accurate discontinuous spline function being analogous to the enrichment of displacement discontinuous modeling, known as the eXtended FEM. The Heaviside B-spline interpolation method enables interpolating jump or discontinuous data in 1-D or 2-D plane by using a least square method : The method interpolates “The Heaviside Step function” with a high accuracy without Gibbs's phenomena. We obtain excellent results for several examples in which the data is given by a discontinuous function.<br />き裂進展問題において重要となるのは，き裂がどのような応力状態で，どの方向へ進展するかである．有限要素法で，き裂進展解析を行う場合の破壊基準として応力による破壊基準を採用するためには，き裂先端近傍の任意の位置で応力を精度良く求める必要がある．一般に有限要素法で求められる応力はガウスの積分点位置のみでの応力値である．その場合，き裂先端近傍の任意の位置の応力を得るためには節点変位を用いて形状関数の一階微分に相当する関数に座標を代入する事で計算する手法，または，ガウス点で取得した応力を用いて内挿補間をする手法などがあげられる．節点変位を用いて応力を算出する場合，変位法に基づく有限要素解析に用いる要素の形状関数は一般にLagrange型の形状関数であり，有限要素解析は多数の要素を配置する事による区分的な補間手法である．したがって，Lagrange型の形状関数を用いた有限要素解析では要素境界において変位の連続性は満たされるが，その微分は不連続であり要素境界において応力やひずみが不連続となる．その場合，要素辺上でき裂進展の破壊基準となる応力が最大となってしまう事があるため有限要素メッシュにより，き裂進展経路が有限要素メッシュに依存する事となる．また，ガウス積分点の応力を用いた内挿補間は補間精度の問題だけでなく，き裂面の上下での応力の不連続が表せない．そこで，一般的に用いられるLagrange型の形状関数を用いた有限要素解析を対象として，ガウス積分点位置で得られる応力を用いて応力を滑らかでかつき裂面上での応力の不連続を高精度に表現可能な新たな補間手法が必要となる．以上の事が本研究を行なった主な動機である．標本データ(例えば，ガウスの積分点で得られる応力など)を滑らかに補間する手法として，B-Splineによる補間手法がある．B-Splineによる補間手法(以下，単にB-Spline補間と表記する．)では，B-Spline補間に用いる節点を多重に配置する事により，Spline関数の連続性を任意に操作ができるため，標本データが不連続となる場合にも有用である．しかし，2次元への拡張を考えた場合，補間対象領域内で標本データが不連続となる曲線(以下，不連続線と表記する)が単純な場合ではなく，任意形状で存在する場合，あるいは，不連続線の1端ないし両端が補間領域内に存在する場合のSpline関数を求める事は容易ではない．2次元のB-Spline基底関数はx，y方向それぞれに対し，一次元のB-Spline基底関数のテンソル積で表されるため，節点は2次元平面上で格子上に配置される．ここで，不連続線を一次元と同様にして考えると不連続線がx軸に対して水平(あるいは垂直)な直線の場合には多重節点により容易に不連続線を表現する事ができる．しかし，不連続線が曲線の場合にはx，y方向節点それぞれに対し，y，x方向に節点配置，多重度が変化させなければならない．すなわち，節点間隔，多重度がx，yの関数となるため節点と格子が一致しない点が存在する．他方，2次元平面上の不連続線を表現する方法として，補間対象領域を分割し，分割領域境界で節点を多重にする事で不連続線を表現する手法が考えられるが，不連続線以外の分割領域では接合条件を与える必要があるなど煩雑である．また，補間領域や不連続線が任意形状の場合には細かな分割が必要となり，B-Spline基底関数を支持する標本データが十分でなくなる場合が生じる．したがって，2次元平面上に標本データがあり，任意の不連続線を高精度に表せるSpline補間が簡易にできる手法が望まれる．本論文ではX-FEM(拡張有限要素法)に用いられる拡張された変位近似式と同様に，Partition of Unity条件に基づきHeaviside関数と不連続パラメータを導入し，任意の不連続線を高精度に表現可能なSpline関数を新たに提案する．提案したSpline関数に対し，最小2乗法を適用する事で不連続パラメータを求める事ができる．本手法をHeaviside B-Spline補間と称する．Heaviside B-Spline補間の有効性を示すために，いくつかの不連続線を有する関数形として、1次元の場合は，階段関数，関数が連続でありその微分が不連続，関数が不連続でかつその微分が不連続な関数を与え，また，2次元の場合は，不連続線が2次元平面上で単一曲線の場合で不連続線が領域内で折れ曲がっている関数をそれぞれ標本データとして与え，補間を行った．その結果，2次元で不連続線が曲線の場合であってもGibbs現象による関数の振動は発生せず，全ての場合で2乗誤差が0となる事を示し，本補間手法の有効性を確認した．
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| 5.
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柳井, 竜 ; 矢富, 盟祥 ; Yanai, Toru ; Yatomi, Chikayoshi
概要:
金沢大学理工研究域環境デザイン学系<br />In this paper, an implicit elasto-plastic finite element analysis at finite strains based on a mu
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ltiplicative decomposition of the deformation gradient is applied to solid/fluid coupling problem. A homogeneous compression tests for a hardening materials under plane strain condition show that the numerical results exhibit a quadratic rate of convergence and are insensitive to the mesh refinement and to the discrete time step. An inhomogeneous example under the compressive displacement exhibits a linear rate of convergence because of using an interpolation approximation of the pore pressure, however, the number of iteration is constant after some time steps. These solutions have a high accuracy in the sense that the equation of motion and continuity condition in the weak sense are satisfied at each model points within a given tolerance and the constitutive equations are satisfied with a high accuracy by the return mapping algorithm.
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| 6.
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志比, 利秀 ; 矢富, 盟祥
概要:
This paper examines the diffuse bifurcation mode of a hollow circular cylinder specimen consisting of a non-coaxial Cam-
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clay model. The specimen undergoes a non-axisymmetric deformation by a prescribed velocity with no friction on the ends and a constant lateral hydrostatic pressure on the side. We obtain several bifurcation loads and examine the sites where the slip planes first occur from the maximum shear strain point of view.<br />出版者照会後に全文公開
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| 7.
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矢富, 盟祥 ; 上田, 拓哉 ; 高木, 慎太郎 ; 阿部, 孝弘
概要:
We present a new numerical path independent Ê-integral for calculating the stress intensity factors using a known auxili
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ary solution. The integral is path independent in the similar manner to the well known domain independent M-integral for calculating the stress intensity factors. The E-integral is, however, path independent even if the path contains any number of crack-tip and the integral may obtain the stress intensity factors at the onset of crack kinking by the path independent integral ; therefore, the integral path can be far from the crack-tip around which the numerical solution has noticeable error : The domain M-integral may not obtain the stress intensity factors at the onset of crack kinking and may be very difficult to obtain the stress intensity factors when there exist small cracks in the neighborhood of the crack-tip. For illustrative purposes, by using finite element method, numerical examples obtaining the stress intensity factors are presented for an extending straight crack and a kinking crack. © 2011 The Society of Materials Science, Japan.
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| 8.
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李, 柄奇 ; 矢富, 盟祥
概要:
Using the X-FEM and the path independent E integral, we analyze the energy release rate at the onset of crack kinking for an isotropic linear elastic material in an infinite plate with a centered crack under a uni-axial and two
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axial compressive loads. In the X-FEM, we propose a simple method in which only the four-node quadrilateral isoperimetric elements in the fractured element are employed without the enrichment by the near-tip asymptotic solution. The friction forces are assumed to follow the Coulomb law, with a slip criterion treated in the context of a standard return mapping algorithm. Consistent linearization of the field equation is performed which leads a fully implicit scheme which preserves asymptotic quadratic convergence of the Newton-Raphson method.
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| 9.
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志比, 利秀 ; 矢富, 盟祥
概要:
This paper examines the diffuse bifurcation mode of a hollow circular cylinder specimen consisting of a non-coaxial Cam-clay model. The specimen undergoes a non-axisymmetric deformation by a prescribed velocity with no friction on the
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ends and a constant lateral hydrostatic pressure on the side. We obtain several bifurcation loads and examine the sites where the slip planes first occur from the maximum shear strain point of view.
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| 10.
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橋本, 堅一 ; 鱸, 洋一 ; 矢富, 盟祥
概要:
Considering the cracks which are related to shear failure in reinforced concrete member model subjected to four point bending, we discuss the extension behavior of fracture cracks by using the maximum energy release rate criterion. For the
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calculation of energy release rate, we use E-integral method by the finite element method.The numerical analyses for some ratios of shear span to effective depth (a/d) are examined. The numerical results arerepresented in the relationship between the energy release rate of shear crack and bending crack for several a/d.It becomes clear that there are two areas which either the energy release rate of shear crack or of bending crack is dominant. The detailed fracture modes of shear failure are also examined for several a/d.
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