两尺度有限元粘塑性颗粒组合体压实模拟

Homogenization based Two scale Finite Element Simulation for Compactions of Visco plastic Granular Assemblies

摘要:

采用一种基于均质化理论的两尺度有限元新方法，模拟粘塑性颗粒组合体的压实全过程，即在细尺度下，通过跟踪颗粒基本单元体（代表体元）的细尺度行为，来生成和更新颗粒组合体的粗尺度本构关系，求得颗粒运动和变形的数学表达式，并考虑了刚体运动与可变形微粒形变之间的耦合，基于此关系式，建立细尺度有限元模型，用以模拟分析颗粒介质在受压过程中的粘塑性细尺度结构行为；在粗尺度下，将颗粒组合体视为均质的连续体，采用粗尺度有限元模型，模拟颗粒组合体的受压过程，数值分析结果与文献实验数据基本一致，验证了该数值方法的准确性和有效性.

Abstract:

A homogenization based two scale finite element method is developed to simulate compactions of visco plastic granular assemblies. The new method is used to develop macro constitutive relationships in light of microscopic behavior. At the microscopic level, governing equations for the motion and deformation of particles, including coupling of rigid body motion and deformation of deformable bodies, are investigated. And an implicit fine scale finite element model for granular media is developed to perform visco plastic analysis for the assemblies. At the global scale level, the homogenized standard continuum is analyzed using a coarse scale finite element model. To verify the accuracy and efficiency of the numerical method, a numerical example is simulated, and the results are in satisfactory agreement with the experimental results in the literature. This method can be used in a variety of problems that can be represented using granular media, such as asphalt, polymers, aluminum, snow, and food products.