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縺ｲ縺壹∩遨ｺ髢灘､夐縺帙ｓ譁ｭ繝｢繝Ν縺ｫ繧医ｋ隱伜ｰ守焚譁ｹ諤ｧ縺ｮ陦ｨ迴ｾEvolution of induced fabric in a strain space multiple mechanism model

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ひずみ空間多重せん断モデルによる誘導異方性の表現

Evolution of Induced Fabric in a Strain Space Multiple Mechanism Model

〇井合 進・飛田哲男

〇Susumu IAI, Tetsuo TOBITA

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this framework, the strain space fabric is defined as a projection of the macroscopic strain field onto an individual virtual simple shear mechanism oriented in arbitrary directions and represents the measure of mobilization of micromechanical strain due to the relative displacements between the particles. The strain space fabric, which is shaped like a four leaf clover in two dimensions, induces another fabric in stress space through a hyperbolic function, which governs the virtual simple shear mechanisms. The stress space fabric represents the measure of mobilization of micromechanical stress due to the contact forces between the particles. With the tensorial average, the stress space fabric produces macroscopic stress. A simulation using Discrete Element Method (DEM) suggests that the strain space multiple mechanism model has the potential to capture the essential features in the evolution of an induced fabric in granular materials.

ひずみ空間多重せん断モデルにおいては，任意 方向の仮想単純せん断機構の重ね合わせにより， 粒状体の力学挙動を表現する。その理論的基礎は， 土粒子間の接点力の体積要素平均として定義され る粒状体の応力と密接な関連がある。本研究では， 同モデルの枠組みで，粒状体の構造を表現する fabric tensor が巨視的な応力場の変化によりどの ように誘導されるかについて，単調せん断と主ひ ずみ軸回転時の挙動について検討するとともに， 主ひずみ軸回転時の主応力軸と主ひずみ軸の非共 軸性について論じる。 ひずみ空間多重せん断モデルの積分形（応力-ひずみ関係）は，接触する土粒子間で定義される branch 方向の単位ベクトルnおよびこれと直交 方向の単位ベクトルtで定義されるdyad を基に， 粒状体の有効応力テンソルσ'とひずみテンソルε を以下の構造を通じて関連づけることにより与え られる。 ' 1 d d 4 p q      I

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t n  (1) t n    t n n t (2) ここに， pは平均有効応力（圧縮を正），Iは identity tensor，qは個々の仮想単純せん断によ る巨視的（平均的）せん断応力への寄与（以下， 仮想単純せん断応力とよぶ）を表す。２重積分の うち，についての積分は仮想単純せん断の機構 の２次元的な集合体を形成する仮想的な平面（n とtの線形関係で定義される平面）内での積分， 立体角についての積分はこれらの平面的な機 構の３次元的な平均を意味するもので，この２重 構造を基に，有効応力が応力誘導異方性を有する ２階の fabric tensor 形式で定義されることが分 かる。 図-1 に，本モデルにより計算された単調せん断 時の誘導異方性を表現する応力ファブリックを示 す。ひずみ空間では，４つ場のクローバー型パタ ーンが変化せずに成長するが，応力空間では，葉 が次第に太っていき，最終的には，単円を４分割 する形で覆いつくす時に，巨視的せん断破壊に達 する。 図-1 巨視的単調せん断時の応力ファブリック

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