Finite strain formulation of a strain space multiple mechanism model for granular materials
Finite strain formulation of a strain space multiple mechanism model for granular materials
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颗粒材料应变空间多机制模型的有限应变公式
DOI：
10.1002/nag.2084
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发表时间：
2012
影响因子：
4
通讯作者：
Tetsuo Tobita and Osamu Ozutsumi
中科院分区：
文献类型：
--
作者：
Susumu Iai;Kyohei Ueda;Tetsuo Tobita and Osamu Ozutsumi
本文给出了颗粒材料应变空间多机制模型的有限应变公式。由于应变空间多机构模型具有合适的细观力学背景，其中分支和互补向量在材料(或参考)坐标中定义，因此有限应变公式是通过跟踪这些向量在方向和大小上与材料中的变形相关的变化来实现的。应用有限应变连续介质力学中建立的可压缩材料的方法，将运动机构分解为体积分量和等容分量，对应变空间多机构模型采用解耦公式。积分形式的拉格朗日描述由第二Piola-Kirchhoff有效应力张量与Green-Lagrange应变张量之间的关系给出，欧拉(空间)描述由柯西有效应力张量与Euler-Almansi应变张量之间的关系给出。特别地，体积应变被定义为雅可比行列式的对数。增量形式的拉格朗日(材料)描述是通过积分形式的材料时间导数得到的。空间描述中的对应关系是通过Lie时间导数导出的，该导数给出了Kirchhoff应力的Oldroyd应力率和变形张量速率(在文献中有时称为拉伸)之间的关系。通过算例讨论了有限应变公式的适用性。版权所有©2012 John Wiley&Sons，Ltd.
This paper presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Because the strain space multiple mechanism model has an appropriate micromechanical background in which the branch and complementary vectors are defined in the material (or referential) coordinate, the finite strain formulation is carried out by following the change in these vectors, in direction and magnitude, associated with deformation in the material. By applying the methodology for compressible materials established in the finite strain continuum mechanics, decoupled formulation that decomposes the kinematic mechanisms into volumetric and isochoric components is adopted for the strain space multiple mechanism model. Lagrangian (material) description of integrated form is given by a relation between the second Piola–Kirchhoff effective stress tensor and the Green–Lagrange strain tensor; Eulerian (spatial) description by a relation between the Cauchy effective stress tensor and the Euler–Almansi strain tensor. In particular, the volumetric strain is defined as a logarithm of Jacobian determinant. Lagrangian (material) description of incremental form is derived through the material time derivative of the integrated form. The counterpart in the spatial description is derived through the Lie time derivative, given as a relation between the Oldroyd stress rate of Kirchhoff stress and the rate of deformation tensor (sometimes called stretching in the literatures). An example is shown to discuss the applicability of the finite strain formulation. Copyright © 2012 John Wiley & Sons, Ltd.
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DOI：
10.1002/nag.899
发表时间：
2011-02
影响因子：
4
作者：
S. Iai;T. Tobita;O. Ozutsumi;K. Ueda
通讯作者：
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影响因子：
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DOI：
10.1002/nag.1610180604
发表时间：
1994
影响因子：
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作者：
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通讯作者：
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影响因子：
3.7
作者：
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DOI：
--
发表时间：
1999
期刊：
--
影响因子：
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作者：
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