Micromechanical study of elastic moduli of three-dimensional granular assemblies
Micromechanical study of elastic moduli of three-dimensional granular assemblies
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DOI：
10.1016/j.ijsolstr.2014.03.002
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发表时间：
2014-06
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
在颗粒材料的细观力学中，研究了颗粒和接触的细观特性与宏观连续特性之间的关系。对于三维各向同性组装体，宏观尺度的弹性模量由体积模量和剪切模量来描述，而体积模量和剪切模量取决于微观尺度的配位数（即每个颗粒的平均接触数）和颗粒间垂直于接触方向和切向接触方向的接触刚度，均匀应变理论（或平均场理论）高估了弹性模量。为了找到更好的预测，近似的粒子位移和旋转场在这里得到的平衡方程求解小的粒子为中心的粒子。在这些边界处，粒子的位移和转动被规定为使它们符合平均场，采用这种方法，得到了改进的体模量和剪切模量的预测，与根据均匀应变假设的结果相比，特别是当尺寸增加的平衡方程求解的颗粒。弹性模量是由颗粒位移，旋转场的两种方法。在第一，基于应力的方法的平均应力张量的微观力学表达式，在接触和分支向量，连接接触中的颗粒的力方面，被采用。在第二种方法中，基于能量的方法，最小势能原理被用来获得严格的上限的模量。通常可以观察到，从应力为基础的方法得到的弹性模量给出更接近的协议从离散元方法模拟的结果比那些从能量为基础的方法。这些改进的弹性模量的预测观察到的范围内的协调数和颗粒间的刚度这里考虑。
In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale continuum characteristics. For three-dimensional isotropic assemblies the macro-scale elastic characteristics are described by the bulk and the shear modulus, which depend on the micro-scale characteristics of the coordination number (i.e. the average number of contacts per particle) and the interparticle contact stiffnesses in directions normal and tangential to the contact.It is well-known that the uniform-strain theory (or mean-field theory) overpredicts the elastic moduli. To find improved predictions, approximations of the particle displacement and rotations fields are obtained here by solving the equilibrium equations for small subassemblies that are centred around particles. At the boundary of these subassemblies, the particle displacements and rotations are prescribed such that they conform to the mean field.Employing this approach, improved predictions of bulk and shear moduli are obtained, in comparison with those according to the uniform-strain assumption, especially when the size is increased of the subassemblies for which equilibrium equations are solved.The elastic moduli are evaluated from the particle displacement and rotations fields by two methods. In the first, stress-based method the micromechanical expression for the average stress tensor, in terms of the forces at contacts and the branch vectors that connect particles in contacts, is employed. In the second, energy-based method the minimum potential-energy principle is used to obtain rigorous upper bounds to the moduli. It is generally observed that the moduli obtained from the stress-based method give closer agreement with the results from Discrete Element Method simulations than those from the energy-based method.These improvements in the predictions of the elastic moduli are observed over the range of coordination numbers and interparticle stiffnesses considered here.