BIFURCATION ANALYSIS AND PATH JUMPING BEHAVIOR OF ELASTO-PLASTIC BODY UNDER COMPRESSION

初期状態において均質な弾塑性材料の供試体が平面ひずみ条件下で圧縮せん断変形を受ける場合について, 有限変形・弾塑性有限要素解析を行い, 分岐モードおよび分岐後の変形挙動や供試体の荷重不安定挙動について考察した. 初期不整を導入した疑似分岐解析ではなく, 完全系の分岐点・分岐モードを求め, 分岐経路への切替えを行った. こうした厳密な分岐解析を行い, 分岐後の変形挙動を追跡することにより, 幾何学的不安定現象としての拡散型分岐モードがせん断帯状の局所変形発生の要因となっていることを検証した. 基本つり合い経路上では一様変形が持続するが, 分岐をきっかけとして不均一な変形が発生し, 次第に局所的な変形へと進展した. また, 初期の変形モードとは異なるモードの経路に段階的に移行するパスジャンプ挙動についても考察を行った.

[1]  Toshihiro Noda,et al.  Imperfection-sensitive bifurcation of cam-clay under plane-strain compression with undrained boundaries , 1995 .

[2]  Kazuo Murota,et al.  Mode switching and recursive bifurcation in granular materials , 1997 .

[3]  J. Bardet.  FINITE ELEMENT ANALYSIS OF PLANE STRAIN BIFURCATION WITHIN COMPRESSIBLE SOLIDS , 1990 .

[4]  Imperfection sensitive strength variation of soil specimens , 1997 .

[5]  M. Goldscheider,et al.  Formation of shear bands in sand bodies as a bifurcation problem , 1978 .

[6]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[7]  Ioannis Vardoulakis,et al.  Bifurcation analysis of the triaxial test on sand samples , 1979 .

[8]  Peter Wriggers,et al.  A quadratically convergent procedure for the calculation of stability points in finite element analysis , 1988 .

[9]  F. Armero,et al.  An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids , 1996 .

[10]  P. Wriggers,et al.  Continuum Mechanics, Nonlinear Finite Element Techniques and Computational Stability , 1993 .

[11]  Toshihiro Noda,et al.  SOIL-WATER COUPLED BEHAVIOUR OF SATURATED CLAY NEAR/AT CRITICAL STATE , 1994 .

[12]  J. Rice,et al.  Finite-element formulations for problems of large elastic-plastic deformation , 1975 .

[13]  Francisco Armero,et al.  Formulation and finite element implementation of a multiplicative model of coupled poro-plasticity at finite strains under fully saturated conditions , 1999 .

[14]  R. de Borst,et al.  Numerical methods for bifurcation analysis in geomechanics , 1989 .

[15]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[16]  John W. Hutchinson,et al.  Bifurcation phenomena in the plane tension test , 1975 .

[17]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[18]  Kazuo Murota,et al.  Recursive Bifurcation as Sources of Complexity in Soil Shearing Behavior , 1997 .

[19]  R. Hill.  The mathematical theory of plasticity , 1950 .

[20]  J. C. Simo,et al.  Numerical analysis and simulation of plasticity , 1998 .

[21]  Richard A. Regueiro,et al.  A finite element model of localized deformation in frictional materials taking a strong discontinuity approach , 1999 .

[22]  Tsutomu Usami,et al.  Three-Dimensional Necking Bifurcation in Tensile Steel Specimens , 2002 .

[23]  Wei Wu.  Non‐linear analysis of shear band formation in sand , 2000 .

[24]  Ioannis Vardoulakis,et al.  GEOMETRIC SOFTENING IN TRIAXIAL TESTS ON GRANULAR MATERIAL , 1982 .

[25]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .