Statics and kinematics of discrete Cosserat-type granular materials
Statics and kinematics of discrete Cosserat-type granular materials
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DOI：
10.1016/s0020-7683(02)00624-8
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发表时间：
2003-02
影响因子：
3.6
通讯作者：
N. P. Kruyt
中科院分区：
文献类型：
--
作者：
N. P. Kruyt
提出了离散coserat型颗粒材料的静力学和运动学的理论框架。与粒子的力和力矩平衡方程类似，在接触处的相对位移和相对旋转的二维情况下，建立了闭环的相容方程。通过对平衡方程取矩，得到了静态量平均柯西应力张量和平均偶应力张量的微力学表达式。同样，通过对相容方程取矩，得到二维情况下（无限小）运动量平均旋转梯度张量和平均Cosserat应变张量的微力学表达式。或者，这些平均柯西应力张量和平均耦合应力张量的表达式是通过考虑作用在一个平面上的连续力和耦合牵引矢量的等价性以及作用在这个平面上的离散力和耦合的合力而得到的。同样，在二维情况下，考虑线素长度的变化和旋转的变化，得到了平均旋转梯度张量和平均Cosserat应变张量的表达式。结果表明，与等效均匀连续体的平均应力张量相反，平均粒子应力张量总是对称的。最后，导出了连续介质力学虚功原理和互补虚功原理的离散类比。
A theoretical framework is presented for the statics and kinematics of discrete Cosserat-type granular materials. In analogy to the force and moment equilibrium equations for particles, compatibility equations for closed loops are formulated in the two-dimensional case for relative displacements and relative rotations at contacts. By taking moments of the equilibrium equations, micromechanical expressions are obtained for the static quantities average Cauchy stress tensor and average couple stress tensor. In analogy, by taking moments of the compatibility equations, micromechanical expressions are obtained for the (infinitesimal) kinematic quantities average rotation gradient tensor and average Cosserat strain tensor in the two-dimensional case. Alternatively, these expressions for the average Cauchy stress tensor and the average couple stress tensor are obtained from considerations of the equivalence of the continuum force and couple traction vectors acting on a plane and the resultant of the discrete forces and couples acting on this plane. In analogy, the expressions for the average rotation gradient tensor and the average Cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two-dimensional case. It is shown that the average particle stress tensor is always symmetrical, contrary to the average stress tensor of an equivalent homogenized continuum. Finally, discrete analogues of the virtual work and complementary virtual work principles from continuum mechanics are derived.